Polynomial Operations Review

Polynomials Review

Multiple Choice

What is the perimeter of the rectangle?

• x²+8x-5

• 2x²+16x-10

• 2x²+10x-8

• 6x-2

Multiple Choice

The profit function P(x), is modeled by P(x) = R(x) - C(x), where R(x) is revenue and C(x) is cost. You own a pencil making company in which your revenue can be modeled as

 $R\left(x\right)\ =\ 4x^2+2x\ -\ 11$  and your cost can be modeled as  $C\left(x\right)\ =\ x^2\ -4$  . Find a function to model your profit. 

•  $P\left(x\right)=3x^2+2x-7$  

•  $P\left(x\right)=3x^2+2x-15$  

•  $P\left(x\right)=5x^2+2x-15$  

•  $P\left(x\right)=5x^3-7$  

Multiple Choice

Simplify each expression.
(6b³ + 6 - b⁴) - (8b³ - 6b⁴ + 2)

• 4b⁴ - 2b³ + 7
• 5b⁴ - 2b³ + 4
• b⁴ - 2b³ + 7
• 5b⁴ - 2b³ + 7

Multiple Choice

Simplify each expression. 
(6x + 4x⁴ - 3x²) + (7x⁴ + 5x² + 8x)

• 11x⁴  + 2x² + 14x
• 16x⁴  + x² + 14x
• 11x⁴  + x² + 14x
• 11x⁴  + 2x² + 10x

Multiple Choice

(5x+2)(x²-3x+6)

• 5x³ - 17x² +24x +12
• 5x³ + 17x² - 24x +12
• 5x³ - 13x² + 24x +12
• 5x³ +13x² - 24x - 12

Multiple Choice

You are an architect designing a rectangular room. The width of the room can be represented by the function $w\left(x\right)=6x-7$  and the length can be measured by the function  $l\left(x\right)=3x-5$  . What is the area of the room?

•  $A\left(x\right)=3x-2$  

•  $A\left(x\right)=9x-12$  

•  $A\left(x\right)=18x^2+51x+35$  

•  $A\left(x\right)=18x^2-51x+35$  

Multiple Choice

Multiply
(x²-2x+1)(x+1)

• x³-x²-x+1
• x³-2x+2
• x³+x²+x+1
• x³-3x²-3x+1

Multiple Choice

 (x − y) ³ 

• x³ − 3x² y + 3xy² − y³
• 16m ⁴ − 32m ³ + 24m ² − 8m + 1 

Multiple Choice

Select the correct expansion of

(1 + x)⁴

• 1 + 4x + 6x² + 4x³ + x⁴

• x + 3x² + 3x³ + x⁴

• 1 + 5x + 10x² + 5x³ + x⁴

• 1 + 2x² + x⁴

Multiple Choice

Which row of Pascal's Triangle would you use to expand (x+y)³?

• 1
• 1  1
• 1  2  1
• 1  3  3  1

Multiple Choice

Divide: 

(4x² - 24x + 35) / (2x - 5)

• 2x - 7
• 2x - 12
• 2x + 12
• 2x + 7

Multiple Choice

Divide.
(12x⁴y⁶  + 24x²y²  - 16 xy) / 4xy

• 3x³y⁵ + 6xy - 4
• 3x⁵y⁷ + 6xy - 4
• 3x⁵y⁵ + 6x³y³ - 4
• 3xy -2

Multiple Choice

Divide using long division

• 2x - 5
• x - 4 + (3/4x - 5)
• 2x + 4 + (3/4x - 5)
• 2x + 4

Multiple Choice

Use synthetic division

• 2x³ + 3x  (7/x-4)
• 2x² + 3x + 8 + (7/x-4)
• 2x² + 3x + 8
• 2x² - x + 10 + (6/x-4)

Multiple Choice

Divide using synthetic division
(2x³ - 5x - 7) ÷ (x - 2)

• 2x³ - 4x² + 3x - 13
• 2x³ + 4x² +3x - 1
• 2x² - 4x + 3 - 13/x-2
• 2x² + 4x + 3 - 1/x-2

Multiple Choice

Find gh(x)

• 2x + 6

• 2x + 3

• 2x² + 6

• 2x² + 3

Multiple Choice

f(x) = 3x² + 7x and g(x) = 2x² - x - 1, find (f - g)(x).

• x² + 8x + 1
• x² + 6x - 1
• 5x² + 8x - 1
• x² + 8x -1

Multiple Choice

(L3) Given f(x)= x² + 25 and g(x)= x - 5, find     (f+g)(x). 

• x² + x - 20
• x² + x + 20
• -x² + x - 20
• x² - x - 20

Multiple Choice

f(x) = x² + 3
g(x) = 4x - 3
Find (fg)(-1)

• 4
• -52
• -4
• 52

Multiple Choice

If f(x) = x² and g(x) = 3x - 1, find f(g(x))

• 9x² - 6x + 1

• 3x - 1

• 3x² - 1

• 9x² - 1

Multiple Choice

Which expression represents g(f(x)) if          f(x) = 2x - 8
and
g(x) = 4x

• 8x - 32
• 8x² - 32x
• 8x - 8
• 6x - 8

Multiple Choice

Find h(g(x))

• 2x + 6

• 2x + 3

• 2x² + 6

• 2x² + 3

Multiple Choice

Given that f(x) = x² + x and g(x) = 3x + 1, find the value of g(f(-2)).

• -14
• 20
• 6
• 7

Multiple Choice

What is f(g(3))?

• 1/8

• 8

• 1/4

• 1/2

Multiple Choice

f(x) = 3x + 10
g(x) = x - 2
Find (f∘g)(0)

• 16
• 4
• -4
• None of these.

Multiple Choice

Given f(x) = 3x + 10
and g(x) = x - 2
Find f(g(5))

• 19
• 23
• -10
• None of these.

Multiple Choice

Which one is the same as fοg(x)

• g(f(x))

• f(g(x))