Deck 5: Polynomials and Polynomial Functions

Question 1

Find the degree of each polynomial and indicate whether the polynomial is a monomial, binomial, trinomial, or none of these.

-4x² - 5x + 7

Answer 1

Trinomial; degree 2

Question 2

Find the degree of each polynomial and indicate whether the polynomial is a monomial, binomial, trinomial, or none of these.
-5x² - 2xy²

Answer 2

Binomial; degree 3

Question 3

Simplify each polynomial by combining like terms.
- $-4y + 9y + 3y^2 - 2y^2 + y$

Answer 3

y²+ 6y

Question 4

Simplify each polynomial by combining like terms.
- $-6xy^2 + 7x - 1/2 + xy^2$

Question 5

Add
-(6y² - 11) + (6y² - 5)

Question 6

Add
-( x² + 5x - 4) + (7x² - 6x - 5)

Question 7

Add
-(8x² - 3x - 1) + (2x + 9)

Question 8

Add
-(2x² - 9) + (3x² - 4x + 3)

Question 9

Add
-(4x² y - 3xy + 7) + (- x² y - 5xy + 8x)

Question 10

Add
-(6.5xyz + 3.2x - y) + (-6.5xyz - 2.1x + y)

Question 11

Subtract.
-(15y² - 3y + 6) - (14 y² - 8y - 1)

Question 12

Subtract.
-(11y² - 7 y + 9) - (3y - 2)

Question 13

Subtract.
- $\left(\frac14x^2 + 6x\right) - \left(\frac34x^2 - \frac15x\right)$

Question 14

Subtract.
-(19ab - 12a²b + 5b²) - (20ab - 8a²b - 4b)

Question 15

Subtract.
-Subtract (2x - 9) from the sum of (14x² + 5x + 3) and (2x - 10x² - 7) .

Question 16

If P(x) = x² + 2x - 5, find each function value.
-P(-1)

Question 17

If P(x) = x² + 2x - 5, find each function value.
-P(4)

Question 18

If P(x) = x² + 2x - 5, find each function value.
-P(0)

Question 19

If P(x) = x² + 2x - 5, find each function value.
-P(-3)

Question 20

If P(x) = x² + 2x - 5, find each function value.
-A projectile is fired upward from the ground with an initial velocity of 250 feet per second. Neglecting air resistance, the height of the projectile at any time t can be described by the polynomial function
P(t) = -16t² + 250t . Find the height at time t = 4 seconds.

Question 21

Multiply.
-(-5x⁴ )(2x² )

Question 22

Multiply.
-4x(6x - 7)

Question 23

Multiply.
--3ab( xa² - ya² - 5)

Question 24

Multiply.
-(2x - 3)(5x² - x + 1)

Question 25

Multiply.
-(a + 5)(4a² - a + 6)

Question 26

Multiply.
-(2 y³ - 7)(3y² + 4 y + 1)

Question 27

Use the FOIL order to multiply
-( x - 2)( x + 8)

Question 28

Use the FOIL order to multiply
-( y - 5)( y - 6)

Question 29

Use the FOIL order to multiply
-(5x + 4)(5x + 1)

Question 30

Use the FOIL order to multiply
- $\left(6x + \frac13\right)\left(9x + \frac12\right)$

Question 31

Use special products to multiply
-( x + 7)²

Question 32

Use special products to multiply
-(3z - 4)²

Question 33

Use special products to multiply
-(8y - 5)(8y + 5)

Question 34

Use special products to multiply
- $\left(4x + \frac12\right)\left(4x - \frac12\right)$

Question 35

Use special products to multiply
-[6 - (2b - 3)]²

Question 36

Multiply.
-( x + y)(3x - 2)( x - 1)

Question 37

Multiply.
-( x - 3)⁴

Question 38

Multiply.
-( x - 4)( x + 4)( x² + 16)

Question 39

If f (x) = x² - x + 1 , find the following.
-f (a+2)

Question 40

If f (x) = x² - x + 1 , find the following.
-f (a-b)

Question 41

Divide
-(10a² + 15a) + 5a

Question 42

Divide
-(24x⁵ 18x³) ÷ 3x2

Question 43

Divide
-

Question 44

Divide
-

Question 45

Divide
-

Question 46

Divide
-

Question 47

Divide
-

Question 48

Divide
-

Question 49

Divide
-

Question 50

Divide
-

Question 51

Divide
-

Question 52

Divide
-(14x³ - 21x² + 4x - 6) ÷ (2x - 3)

Question 53

Divide
-(6x³ - 8x² + 3x - 6) ÷ (3x - 4)

Question 54

Use synthetic division to divide.
-( x² + 3x - 54) ÷ ( x - 6)

Question 55

Use synthetic division to divide.
-( x³ - 5x² - 2x + 19) ÷ ( x - 2)

Question 56

Use synthetic division to divide.
-(5x² + 6) ÷ ( x - 1)

Question 57

Use synthetic division to divide.
-(4x⁴ + 19x³ - 7x² - 9x + 7) ÷ ( x + 5)

Question 58

Use synthetic division to divide.
-(7x⁴ + 30x³ - 30x - 10) ÷ ( x + 4)

Question 59

Use synthetic division to divide.
- $(3x^3 + 4x^2 - 7x + 2) \div \left(x - \frac23\right)$

Question 60

Use synthetic division to divide.
- $\frac{y^3 - 27}{y - 3}$

Question 61

Factor out the greatest common factor.
-16x - 24

Question 62

Factor out the greatest common factor.
-6y - 18y³

Question 63

Factor out the greatest common factor.
-12 x⁵ - 18x⁴ + 3x²

Question 64

Factor out the greatest common factor.
-10y - 20y² + 15y³

Question 65

Factor out the greatest common factor.
-16a³b³ - 4a²b³ + 4ab² - 24ab³

Question 66

Factor out the greatest common factor.
-14x³ y² - 28x² y³ + 7x² y² - 7xy

Question 67

Factor out the greatest common factor.
-9( x + 2) + 2 x( x + 2)

Question 68

Factor out the greatest common factor.
-3x( y - 3) + ( y - 3)

Question 69

Factor out the greatest common factor.
-5x(3y - 8) - 7(3y - 8)

Question 70

Factor out the greatest common factor.
-The material needed to manufacture a box with two square ends is given by the polynomial $2x^2 + 4xy$ , where x is the length of the square ends and y is the length of the other sides. Factor this polynomial

Question 71

Factor out the greatest common factor.
-An object shot from the ground with an initial velocity of 80 feet per second has a height of $-16t^2 + 80t$ feet after t seconds. Factor this polynomial.

Question 72

Factor each polynomial by grouping.
-xy + 2 x + 6 y + 12

Question 73

Factor each polynomial by grouping.
-ab + 2a - 5b - 10

Question 74

Factor each polynomial by grouping.
-8xy + 4x - 6y - 3

Question 75

Factor each polynomial by grouping.
-21x² - 14x - 6x + 4

Question 76

Factor each polynomial by grouping.
-x³ - 4x² - 3x + 12

Question 77

Factor each polynomial by grouping.
-5x² + 15x + 2xy + 6y

Question 78

Factor each polynomial by grouping.
-12x² - 8x + 9xy - 6y

Question 79

Factor.
-xy⁴ - 3xy - y⁴ + 3y

Question 80

Factor.
--8x² y -12xy + 4x