Question 1

Factor the expression completely, if possible. Rewrite the expression in standard form and factor out "-1" if needed. If you believe the trinomial will not factor, answer "prime." x² + 2x + 3 A) (x + 3)(x + 1) B) (x - 3)(x - 1) C) (x + 2)(x + 1) D) prime

Accepted Answer

The trinomial does not appear to have any common factors, and it cannot be factored using any common factoring methods. Therefore, it is prime, which means it cannot be factored any further.

Question 2

Factor the trinomial completely. x² - 18x + 80 A) (x + 8)(x + 10) B) (x - 8)(x + 10) C) (x + 1)(x + 80) D) (x - 8)(x - 10)

Accepted Answer

The correct factoring of the trinomial $x^2 - 18x + 80$ is $(x - 8)(x - 10)$, as both factors multiply to give $x^2 - 18x + 80$.

Question 3

Reduce to lowest terms.

Accepted Answer

The answer of Reduce to lowest terms. ...

Question 4

Factor the expression completely, if possible. Rewrite the expression in standard form and factor out "-1" if needed. If you believe the trinomial will not factor, answer "prime." x³ - 4x² - 4x + 16

Accepted Answer

The answer of Factor the expression completely, if possible. Rewrite...

Question 5

Reduce to lowest terms.

Accepted Answer

The answer of Reduce to lowest terms. ...

Question 6

Factor the trinomial completely. x² + x - 56

Accepted Answer

The answer of Factor the trinomial completely. x² + x...

Question 7

Reduce to lowest terms. 
A) 1
B) -1
C) 
D)

Accepted Answer

The answer of Reduce to lowest terms. 
A) 1
B) -1
C)...

Question 8

Factor the expression completely, if possible. Rewrite the expression in standard form and factor out "-1" if needed. If you believe the trinomial will not factor, answer "prime." x² + 17x + 70 A) (x - 10)(x - 7) B) (x + 10)(x + 7) C) (x + 1)(x + 70) D) (x + 10)(x - 7)

Accepted Answer

The expression x^2 + 17x + 70 factors into (x + 10)(x + 7) because 10 and 7 are factors of 70 that add up to 17.

Question 9

Factor the difference of perfect cubes completely. 27a³ - 1000 A) (3a + 10)(9a² - 100) B) (3a - 10)(9a² + 100) C) (3a + 10)(9a² - 30a + 100) D) (3a - 10)(9a² + 30a + 100)

Accepted Answer

The difference of perfect cubes can be factored using the formula $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$. Here, $27a^3 = (3a)^3$ and $1000 = 10^3$, so the factorization is $(3a - 10)((3a)^2 + 3a*10 + 10^2)$, which simplifies to $(3a - 10)(9a^2 + 30a + 100)$.

Question 10

Factor the expression completely, if possible. Rewrite the expression in standard form and factor out "-1" if needed. If you believe the trinomial will not factor, answer "prime." 8a³ + 27 A) (2a - 3)(4a + 9) B) (2a - 3)(4a + 6a + 9) C) (2a + 3)(4a - 6a + 9) D) (2a - 3)(4a - 6a + 9)

Accepted Answer

The expression 8a^3 + 27 is a sum of cubes, which can be factored as (2a + 3)(4a^2 - 6a + 9).

Question 11

Factor by grouping. x⁵+ 3x³ - 5x² - 15

Accepted Answer

The answer of Factor by grouping. x⁵+ 3x³ -...

Question 12

Factor the perfect square trinomial completely. 9x² + 30x + 25 A) (3x + 5)² B) (3x - 5)(3x + 5) C) (9x + 5)(x + 5) D) (3x + 1 )(3x + 25)

Accepted Answer

The given trinomial is a perfect square because it can be written as (3x + 5)^2, where the first term (9x^2) is a square of 3x, the last term (25) is a square of 5, and the middle term (30x) is twice the product of 3x and 5.

Question 13

Factor the trinomial completely. 9x² - 30x + 25 A) (3x - 5)(3x - 5) B) (3x + 5)(3x + 5) C) (9x - 5)(x - 5) D) (3x + 1)(3x + 25)

Accepted Answer

The trinomial can be factored as a perfect square, $ (3x)^2 - 2(3x)(5) + 5^2 $, which simplifies to $ (3x - 5)^2 $ or $ (3x - 5)(3x - 5) $.

Question 14

Reduce to lowest terms. 
A) 
B) 
C) 
D)

Accepted Answer

To reduce the fraction to lowest terms, we need to divide both the numerator and denominator by their greatest common factor. In this case, the greatest common factor of the numerator and denominator is 11, so we can divide both by 11 to get:
ea7f29_4f93_4678_9ecd_6b5190a0557b_TB3307_11
Therefore, the answer is choice D.

Question 15

Factor the expression completely, if possible. Rewrite the expression in standard form and factor out "-1" if needed. If you believe the trinomial will not factor, answer "prime." -21x² + 6x + 15x³

Accepted Answer

The answer of Factor the expression completely, if possible. Rewrite...

Question 16

Factor the trinomial completely. 3x² + 20x + 25

Accepted Answer

The answer of Factor the trinomial completely. 3x² + 20x...

Question 17

Factor out the common binomial factor. 10x(x - 5) - 7(x - 5)

Accepted Answer

The answer of Factor out the common binomial factor. 10x(x...

Question 18

Factor the perfect square trinomial completely. x² - 6x + 9

Accepted Answer

The answer of Factor the perfect square trinomial completely. x²...

Question 19

Factor using u-substitution. 36 + x⁴ - 13x²

Accepted Answer

The answer of Factor using u-substitution. 36 + x⁴ -...

Question 20

Factor the difference of perfect squares completely. 9x² - 16

Accepted Answer

The answer of Factor the difference of perfect squares completely....

Quiz 12: Review of Basic Concepts and Skills

Factor the expression completely, if possible. Rewrite the expression in standard form and factor out "-1" if needed. If you believe the trinomial will not factor, answer "prime." x2 + 2x + 3

Factor the trinomial completely. x2 - 18x + 80

Reduce to lowest terms.

Factor the expression completely, if possible. Rewrite the expression in standard form and factor out "-1" if needed. If you believe the trinomial will not factor, answer "prime." x3 - 4x2 - 4x + 16

Reduce to lowest terms.

Factor the trinomial completely. x2 + x - 56

Reduce to lowest terms.

Factor the expression completely, if possible. Rewrite the expression in standard form and factor out "-1" if needed. If you believe the trinomial will not factor, answer "prime." x2 + 17x + 70

Factor the difference of perfect cubes completely. 27a3 - 1000

Factor the expression completely, if possible. Rewrite the expression in standard form and factor out "-1" if needed. If you believe the trinomial will not factor, answer "prime." 8a3 + 27

Factor by grouping. x5 + 3x3 - 5x2 - 15

Factor the perfect square trinomial completely. 9x2 + 30x + 25

Factor the trinomial completely. 9x2 - 30x + 25

Reduce to lowest terms.

Factor the expression completely, if possible. Rewrite the expression in standard form and factor out "-1" if needed. If you believe the trinomial will not factor, answer "prime." -21x2 + 6x + 15x3

Factor the trinomial completely. 3x2 + 20x + 25

Factor out the common binomial factor. 10x(x - 5) - 7(x - 5)

Factor the perfect square trinomial completely. x2 - 6x + 9

Factor using u-substitution. 36 + x4 - 13x2

Factor the difference of perfect squares completely. 9x2 - 16

Factor the expression completely, if possible. Rewrite the expression in standard form and factor out "-1" if needed. If you believe the trinomial will not factor, answer "prime." x² + 2x + 3

Factor the trinomial completely. x² - 18x + 80

Factor the expression completely, if possible. Rewrite the expression in standard form and factor out "-1" if needed. If you believe the trinomial will not factor, answer "prime." x³ - 4x² - 4x + 16

Factor the trinomial completely. x² + x - 56

Factor the expression completely, if possible. Rewrite the expression in standard form and factor out "-1" if needed. If you believe the trinomial will not factor, answer "prime." x² + 17x + 70

Factor the difference of perfect cubes completely. 27a³ - 1000

Factor the expression completely, if possible. Rewrite the expression in standard form and factor out "-1" if needed. If you believe the trinomial will not factor, answer "prime." 8a³ + 27

Factor by grouping. x⁵+ 3x³ - 5x² - 15

Factor the perfect square trinomial completely. 9x² + 30x + 25

Factor the trinomial completely. 9x² - 30x + 25

Factor the expression completely, if possible. Rewrite the expression in standard form and factor out "-1" if needed. If you believe the trinomial will not factor, answer "prime." -21x² + 6x + 15x³

Factor the trinomial completely. 3x² + 20x + 25

Factor the perfect square trinomial completely. x² - 6x + 9

Factor using u-substitution. 36 + x⁴ - 13x²

Factor the difference of perfect squares completely. 9x² - 16