Question 1

Choose the one alternative that best completes the statement or answers the question.Find the product. -( 5m⁴z⁴⁾( 5m³z²) A) 25mz⁷ B) 25m⁷z⁶ C) 25m⁷z D) 25mz⁶

Accepted Answer

To find the product, multiply the coefficients and add the exponents of like bases: (5 * 5)m^(4+3)z^(4+2) = 25m^7z^6.

Question 2

Choose the one alternative that best completes the statement or answers the question.Find the product. -( -3m³z⁴)( 3m²z²) A) -9m⁵z⁶ B) -9m⁶z⁵ C) -9mz⁵ D) -9mz⁶

Accepted Answer

Multiplying the two expressions involves multiplying the coefficients (-3 and 3) to get -9, and adding the exponents of like variables (m and z) according to the laws of exponents. This results in $m^{13+12} = m^{25}$ and $z^{14+12} = z^{26}$, making the correct answer -9m^25z^26.

Question 3

Choose the one alternative that best completes the statement or answers the question.Find the product. -( -4x⁴y⁴)( -5x³y²) A) 20xy⁶ B) 20x⁶y⁷ C) 20x⁷y⁶ D) 20xy⁷

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 4

Choose the one alternative that best completes the statement or answers the question.Find the product.
-6( -7x + 10)
A) -42x + 60
B) -7x + 60
C) -42x + 10
D) 18x

Accepted Answer

To find the product, distribute 6 to both terms inside the parentheses: 6 * (-7x) = -42x and 6 * 10 = 60, resulting in -42x + 60.

Question 5

Choose the one alternative that best completes the statement or answers the question.Find the product. --3x( -4x - 12) A) 48x² B) -4x² + 36x C) 12x² + 36x D) 12x² - 12x

Accepted Answer

The product is found by distributing -3x to each term inside the parentheses: -3x(-4x) = 12x^2 and -3x(-12) = 36x. Thus, the expression simplifies to 12x^2 + 36x.

Question 6

Choose the one alternative that best completes the statement or answers the question.Find the product. -3x²( 9x + 8) A) 27x³ + 24x² B) 27x + 24 C) 51x² D) 27x³ + 8

Accepted Answer

The correct answer is obtained by distributing the term $3x$ across the binomial $(9x + 8)$, resulting in $27x^2 + 24x$.

Question 7

Choose the one alternative that best completes the statement or answers the question.Find the product. --9x⁶( 12x⁷ - 2) A) -108x⁷ + 18 B) -108x¹³ + 18x⁶ C) -90x⁶ D) -108x¹³ - 2

Accepted Answer

The product is found by distributing -9x^6 to each term inside the parentheses: -9x^6 * 12x^7 = -108x^13 and -9x^6 * (-2) = 18x^6.

Question 8

Choose the one alternative that best completes the statement or answers the question.Find the product. --8x⁶( 11x⁷ - 7x⁴) A) -88x¹³ + 56x¹⁰ B) -88x¹³ - 7x⁴ C) -32x⁶ D) -32x¹³ - 32x¹⁰

Accepted Answer

The correct answer is obtained by multiplying -8x by each term inside the parentheses, applying the distributive property, and combining like terms correctly.

Question 9

Choose the one alternative that best completes the statement or answers the question.Find the product. -8x²( 12x⁴ - 12x³) A) 96 - 96 B) 96 + 96 C) 96 - 12 D) 96 - 96x

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 10

Choose the one alternative that best completes the statement or answers the question.Find the product. -5x⁴( -6x⁷ + 8x² + 10) A) -30x¹¹ + 40x⁶ B) -30x¹¹ + 8x² + 10 C) -30x⁷ + 40x² + 50 D) -30x¹¹ + 40x⁶ + 50x⁴

Accepted Answer

Multiplying $5x^{14}$ by each term in the parentheses gives $-30x^{31} + 40x^{26} + 50x^{14}$.

Question 11

Choose the one alternative that best completes the statement or answers the question.Find the product. --12x⁵( 4x⁶ + 6x² + 10) A) -48x⁶ - 72x² - 120 B) -48x¹¹ - 72x⁷ C) -48x¹¹ + 6x² + 10 D) -48x¹¹ - 72x⁷ - 120x⁵

Accepted Answer

The product is found by distributing -12x^5 to each term inside the parentheses: -12x^5 * 4x^6 = -48x^11, -12x^5 * 6x^2 = -72x^7, and -12x^5 * 10 = -120x^5.

Question 12

Choose the one alternative that best completes the statement or answers the question.Find the product. --6^x⁵( -11^x⁸ - 12x⁴⁺¹⁰⁾ A) 66^x¹³ + 72^x⁹ + 10 B) 66^x¹³ - 12x⁴⁺¹⁰ C) 66^x⁸ + 72x⁴^-⁶⁰ D) 66^x¹³ + 72^x⁹ - 60^x⁵

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 13

Choose the one alternative that best completes the statement or answers the question.Find the product. -7x²y( -9x⁶y + 6x³) A) -63x⁸y²+ 42x⁵ B) -63x⁸y²+ 42x⁵y C) -63xy + 42x D) -63x⁸y²+ 6x³

Accepted Answer

When multiplying the given expressions, the coefficients are multiplied together, and the exponents of like bases are added. The correct product is -63x^18y^12 + 42x^15y, which matches choice B.

Question 14

Choose the one alternative that best completes the statement or answers the question.Find the product. -( 9p - 1)( 81p² + 9p + 1) A) 729p³ - 1 B) 729p³ + 1 C) 81p³ - 1 D) 729p³ + 90p² - 1

Accepted Answer

The product of (9p - 1) and (81p^2 + 9p + 1) can be found using the distributive property (also known as the FOIL method for binomials). Multiplying the terms, we get 729p^3 - 1, since the middle terms (729p^2 and -9p) cancel out.

Question 15

Choose the one alternative that best completes the statement or answers the question.Find the product. -( 5y - 4)( 25y²⁺^20y⁺¹⁶⁾ A) 125y³⁺⁶⁴ B) 125y³+ 80y² - 64 C) 25y³⁺⁶⁴ D) 125y³^-⁶⁴

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 16

Choose the one alternative that best completes the statement or answers the question.Find the product. -( 5x² - 4x - 3)(x² + 3x - 1) A) 5x⁴ + 15x³ - 17x² - 5x + 3 B) 5x⁴ + 15x³ - 20x² - 5x + 3 C) 5x⁴ + 11x³ - 20x² - 5x + 3 D) 5x⁴ + 11x³ - 17x² - 5x + 3

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 17

Choose the one alternative that best completes the statement or answers the question.Find the product. -( 3 z² + 3 z + 5)( z² + 5 z + 2) A) 3 z⁴ + 18 z³ + 26 z² + 31 z + 10 B) 3 z⁴ + 18 z³ + 21 z² + 31 z + 10 C) 3 z⁴ + 15 z³ + 21 z² + 31 z + 10 D) 3 z⁴ + 15 z³ + 26 z² + 31 z + 10

Accepted Answer

The correct answer is obtained by multiplying the polynomials together, following the distributive property (also known as FOIL for binomials). Each term in the first polynomial is multiplied by each term in the second polynomial, and then like terms are combined. The coefficients and powers of z are carefully calculated to ensure accuracy, leading to the correct expansion and simplification as shown in option A.

Question 18

Choose the one alternative that best completes the statement or answers the question.Find the product. -( 4 k - 5)( 2 k³ - 3 k² + 5 k + 4) A) 8 k⁴ + 3 k³ + 35 k² - 9 k - 20 B) 8 k⁴ - 22 k³ + 35 k² - 9 k - 20 C) 8 k⁴ - 22 k³ + 35 k² + 16 k - 20 D) 8 k⁴ - 22 k³ - 5 k² - 9 k - 20

Accepted Answer

To find the product of $ (4k - 5)(2k^3 - 3k^2 + 5k + 4) $, you distribute each term in the first polynomial across the second polynomial. This involves multiplying $4k$ by each term in the second polynomial and then $ -5$ by each term in the second polynomial, and finally adding the results together. The correct distribution and combination of like terms yield $8k^4 - 22k^3 + 35k^2 - 9k - 20$.

Question 19

Choose the one alternative that best completes the statement or answers the question.Find the product.
-( 3x - 1)( 4  - 3  + 4  - x + 4)
A) 12- 4  - 9  + 15  - 7  + 13x - 4 
B) 12- 4  - 9  + 9  - 7  + 11x + 4 
C) 12- 4  - 9  + 15  + 13x - 4 
D) 12- 9  + 12  - 3  + 12x - 1

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 20

Choose the one alternative that best completes the statement or answers the question.Find the product.
-( 15  - 25  + 30x) 
A) 3  - 135  + 5  + 219  - 270x
B) 15  - 25  + 6x + 9
C) 3  + 135  - 5  - 219  + 270x
D) 3  + 135  - 5  + 276x

Accepted Answer

The answer of Choose the one alternative that best completes...

Quiz 6: Factoring and Applications

Choose the one alternative that best completes the statement or answers the question.Find the product. -( 5m⁴z⁴⁾( 5m³z²)

Choose the one alternative that best completes the statement or answers the question.Find the product. -( -3m³z⁴) ( 3m²z²)

Choose the one alternative that best completes the statement or answers the question.Find the product. -( -4x⁴y⁴) ( -5x³y²)

Choose the one alternative that best completes the statement or answers the question.Find the product. -6( -7x + 10)

Choose the one alternative that best completes the statement or answers the question.Find the product. --3x( -4x - 12)

Choose the one alternative that best completes the statement or answers the question.Find the product. -3x²( 9x + 8)

Choose the one alternative that best completes the statement or answers the question.Find the product. --9x⁶( 12x⁷ - 2)

Choose the one alternative that best completes the statement or answers the question.Find the product. --8x⁶( 11x⁷ - 7x⁴)

Choose the one alternative that best completes the statement or answers the question.Find the product. -8x²( 12x⁴ - 12x³)

Choose the one alternative that best completes the statement or answers the question.Find the product. -5x⁴( -6x⁷ + 8x² + 10)

Choose the one alternative that best completes the statement or answers the question.Find the product. --12x⁵( 4x⁶ + 6x² + 10)

Choose the one alternative that best completes the statement or answers the question.Find the product. --6^x⁵( -11^x⁸ - 12x⁴⁺¹⁰⁾

Choose the one alternative that best completes the statement or answers the question.Find the product. -7x²y( -9x⁶y + 6x³)

Choose the one alternative that best completes the statement or answers the question.Find the product. -( 9p - 1) ( 81p² + 9p + 1)

Choose the one alternative that best completes the statement or answers the question.Find the product. -( 5y - 4) ( 25y²⁺^20y⁺¹⁶⁾

Choose the one alternative that best completes the statement or answers the question.Find the product. -( 5x² - 4x - 3) (x² + 3x - 1)

Choose the one alternative that best completes the statement or answers the question.Find the product. -( 3 z² + 3 z + 5) ( z² + 5 z + 2)

Choose the one alternative that best completes the statement or answers the question.Find the product. -( 4 k - 5) ( 2 k³ - 3 k² + 5 k + 4)

Choose the one alternative that best completes the statement or answers the question.Find the product. -( 3x - 1) ( 4 - 3 + 4 - x + 4)

Choose the one alternative that best completes the statement or answers the question.Find the product. -( 15 - 25 + 30x)

Quiz 6: Factoring and Applications

Choose the one alternative that best completes the statement or answers the question.Find the product. -( 5m4z4) ( 5m3z2)

Choose the one alternative that best completes the statement or answers the question.Find the product. -( -3m3z4) ( 3m2z2)

Choose the one alternative that best completes the statement or answers the question.Find the product. -( -4x4y4) ( -5x3y2)

Choose the one alternative that best completes the statement or answers the question.Find the product. -6( -7x + 10)

Choose the one alternative that best completes the statement or answers the question.Find the product. --3x( -4x - 12)

Choose the one alternative that best completes the statement or answers the question.Find the product. -3x2( 9x + 8)

Choose the one alternative that best completes the statement or answers the question.Find the product. --9x6( 12x7 - 2)

Choose the one alternative that best completes the statement or answers the question.Find the product. --8x6( 11x7 - 7x4)

Choose the one alternative that best completes the statement or answers the question.Find the product. -8x2( 12x4 - 12x3)

Choose the one alternative that best completes the statement or answers the question.Find the product. -5x4( -6x7 + 8x2 + 10)

Choose the one alternative that best completes the statement or answers the question.Find the product. --12x5( 4x6 + 6x2 + 10)

Choose the one alternative that best completes the statement or answers the question.Find the product. --6x5( -11x8 - 12x4 + 10)

Choose the one alternative that best completes the statement or answers the question.Find the product. -7x2 y( -9x6y + 6x3)

Choose the one alternative that best completes the statement or answers the question.Find the product. -( 9p - 1) ( 81p2 + 9p + 1)

Choose the one alternative that best completes the statement or answers the question.Find the product. -( 5y - 4) ( 25y2 + 20y + 16)

Choose the one alternative that best completes the statement or answers the question.Find the product. -( 5x2 - 4x - 3) (x2 + 3x - 1)

Choose the one alternative that best completes the statement or answers the question.Find the product. -( 3 z2 + 3 z + 5) ( z2 + 5 z + 2)

Choose the one alternative that best completes the statement or answers the question.Find the product. -( 4 k - 5) ( 2 k3 - 3 k2 + 5 k + 4)

Choose the one alternative that best completes the statement or answers the question.Find the product. -( 3x - 1) ( 4 - 3 + 4 - x + 4)

Choose the one alternative that best completes the statement or answers the question.Find the product. -( 15 - 25 + 30x)

Choose the one alternative that best completes the statement or answers the question.Find the product. -( 5m⁴z⁴⁾( 5m³z²)

Choose the one alternative that best completes the statement or answers the question.Find the product. -( -3m³z⁴) ( 3m²z²)

Choose the one alternative that best completes the statement or answers the question.Find the product. -( -4x⁴y⁴) ( -5x³y²)

Choose the one alternative that best completes the statement or answers the question.Find the product. -3x²( 9x + 8)

Choose the one alternative that best completes the statement or answers the question.Find the product. --9x⁶( 12x⁷ - 2)

Choose the one alternative that best completes the statement or answers the question.Find the product. --8x⁶( 11x⁷ - 7x⁴)

Choose the one alternative that best completes the statement or answers the question.Find the product. -8x²( 12x⁴ - 12x³)

Choose the one alternative that best completes the statement or answers the question.Find the product. -5x⁴( -6x⁷ + 8x² + 10)

Choose the one alternative that best completes the statement or answers the question.Find the product. --12x⁵( 4x⁶ + 6x² + 10)

Choose the one alternative that best completes the statement or answers the question.Find the product. --6^x⁵( -11^x⁸ - 12x⁴⁺¹⁰⁾

Choose the one alternative that best completes the statement or answers the question.Find the product. -7x²y( -9x⁶y + 6x³)

Choose the one alternative that best completes the statement or answers the question.Find the product. -( 9p - 1) ( 81p² + 9p + 1)

Choose the one alternative that best completes the statement or answers the question.Find the product. -( 5y - 4) ( 25y²⁺^20y⁺¹⁶⁾

Choose the one alternative that best completes the statement or answers the question.Find the product. -( 5x² - 4x - 3) (x² + 3x - 1)

Choose the one alternative that best completes the statement or answers the question.Find the product. -( 3 z² + 3 z + 5) ( z² + 5 z + 2)

Choose the one alternative that best completes the statement or answers the question.Find the product. -( 4 k - 5) ( 2 k³ - 3 k² + 5 k + 4)