Polynomial Review

Polynomial Review

Unit Test Review

Factoring Review

Multiple Choice

Which method of factoring should be used for...

 $x^{4\ }+5x^{2\ }-36$  

• Difference of Squares

• Sum of Cubes

• Factoring by Grouping

• X Method

Multiple Choice

Which method of factoring should be used for...

 $x^{2\ }+9$  

• Difference of Squares

• Sum of Cubes

• Factoring by Grouping

• Can't be factored

Multiple Choice

Which method of factoring should be used for...

 $18x^3+27x^2-8x-12$  

• Difference of Squares

• Sum of Cubes

• X - Method

• Factoring by Grouping

Multiple Choice

Which method of factoring should be used for...

 $8x^3+\ 1$  

• Difference of Squares

• Sum of Cubes

• X - Method

• Factoring by Grouping

Multiple Choice

Which method of factoring should be used for...

 $x^3-\ 27$  

• Difference of Squares

• Difference of Cubes

• X - Method

• Factoring by Grouping

Multiple Choice

Which method of factoring should be used for...

 $x^2-\ 9$  

• Difference of Squares

• Difference of Cubes

• X - Method

• Factoring by Grouping

4 Term Factoring

Multiple Choice

Factor

2x³-8x²-x+4

• (2x²-1)(x-4)

• 2(x²-1)(x+4)

• (x²-1)(2x-4)

• (2x²+1)(x-4)

Multiple Choice

Factor

7r³-8r²+42r-48

• (r²+6)(7r+8)

• (r²+6)(7r-8)

• (r²+6)(r²+8)

• (r²+6)(7r+6)

Factoring 3 Terms!

Multiple Choice

Factor

3x³ - 17x² + 20x

• (3x + 4)(x - 5)

• x(3x - 5)(x - 4)

• x(3x + 4)(x - 5)

• (3x - 4)(x - 5)

Multiple Choice

Factor.

 $x^3-6x^2-40x$  

•  $x\left(x+4\right)\left(x-10\right)$  

•  $\left(x+4\right)\left(x-10\right)$  

•  $\left(x+20\right)\left(x-2\right)$  

•  $x\left(x-4\right)\left(x-10\right)$  

Factoring 2 Terms

Multiple Choice

Factor

8x³ + 27

• (3x - 2)(9x² + 6x + 4)

• (3x - 1)(9x² + 3x + 1)

• (2x + 3)(4x² - 6x + 9)

• (2x - 1)(4x² + 2x + 1)

Multiple Choice

Factor

 $x^{3\ }-\ 27$  

•  $\left(x-3\right)\left(x^{2\ }+3x+9\right)$  

•  $\left(x+3\right)\left(x^{2\ }+3x+9\right)$  

•  $\left(x-3\right)\left(x^{2\ }-3x+9\right)$  

Multiple Choice

Factor completely:
2x³ + 5x² - 8x - 20

• (x² - 4)(2x + 5)
• (2x - 5)(x² + 4)
• (2x² - 4)(x + 5)
• (x - 2)(x + 2)(2x + 5)

Polynomial Graphs

Multiple Choice

What are the decreasing intervals?

• (- ∞, 0) & (2, ∞ )

• (-1, 0) & (2,-4)

• (0,2)

• (0, -4) & (0, 2)

Multiple Choice

What are the increasing intervals?

• (- ∞, 0) & (2, ∞ )

• (-1, 0) & (2,4)

• (0,2) & (-3, -7)

• (-8, -3) & (-7, 8)

Multiple Choice

Which of the following correctly identifies the End Behavior?

Multiple Choice

State the Range.

• y ≤ 0

• y ≥ 0

• All Reals

• y ≤ - 4

Multiple Choice

What are the
zeros of the polynomial
y = 3(x + 4)(x + 1)(x - 3)?

• -4, -1, 3
• 3, -3, 4, 1
• 4, 1, -3
• 3, -4, -1, 3

Multiple Choice

Even or Odd degree?

• even

• odd

Multiple Choice

• y = x(x - 3)(x - 2)
• y = x(x - 3)² (x+2)
• y = x(x + 3)² (x - 2)
• y = -x(x + 3)² (x - 2)

Multiple Choice

Which equation matches the graph?

• y = ^_(x + 2)(x - 1)²

• y = -(x - 2)(x + 1)²

• y = (x - 2)(x + 1)²

• y = -x³

Transformations of Cubic Functions

 $y=a\left(x-h\right)^3+k$  

Multiple Choice

The graph shows the function f(x)=x³ in blue and another function g(x) in red.  Which could be the equation for g(x)?

• A.  g(x) = -x³
• B.  g(x) = x³ - 1
• C.  g(x) = (x + 1)³
• D.  g(x) = (x - 1)³

Multiple Choice

Describe the transformation of the graph  y = - ½(x + 4)³ - 1

• Left 4 and Down 1
• Reflected x-axis, Down 1, Left 4, Shrink by 1/2
• Reflected x-axis, Down 1, Left 4, Stretch by 1/2
• Reflected x-axis, Up 1, Right 4, Shrink by 1/2

Multiple Choice

Describe the transformation of the graph y = -2(x + 5)³

• Compress by 2, Reflected over y-axis, Right 5

• Stretch by 2, Reflected over x-axis, Left 5

• Stretch by 2, Reflected over x-axis, Right 5

• Compress by 2, reflected over y-axis, Left 5

Multiple Choice

Describe the transformations of the graph y = (x - 3)³ -2

• Right 3, Down 2
• Left 3, Up 2
• Right 3, Up 2
• Left 3, Down 2 

Add, Subtract, Multiply and Divide Polynomials

Multiple Choice

Find the sum.
(3y² + y³ - 5) + (4y² -4y + 2y³ + 8)

• 3y³ + 7y² - 4y + 3
• 4y² + 3y³ - y + 3
• -y⁴ + 2y³ -y - 4
• 4y³ + 3y² -3y + 1

Multiple Choice

Simplify

(5x⁴ - 4x³ - 2x² + x - 19) - (x⁴ + 5x³ + 8x² + x + 5)

• 4x⁴ - 9x³ - 10x² - 24

• 4x⁴ - 9x³ - 10x² - 2x - 24

• 4x⁴ - 9x³ - 10x² + 2x - 24

• -4x⁴ - 9x³ - 10x² - 24

Multiple Choice

Multiply

(2x + 3)(x² + 4x + 1)

• 2x³ + 10x² + 14x + 4

• 2x³ + 11x² + 14x + 3

• -2x³ - 11x² + 14x + 5

• x³ - 11x² + 14x + 3

Multiple Choice

Divide using long division. $\left(x^3+3x^2-x+2\right)\div\left(x-1\right)$   

•  $x^2+4x+3-\frac{5}{x-1}$  

•  $x^2+4x+3+\frac{5}{x-1}$  

•  $x^2-4x+3+\frac{5}{x-1}$  

•  $x^2-4x-3-\frac{5}{x-1}$  

Multiple Choice

Divide using long division. $\left(x^2-3x-40\right)\div\left(x+5\right)$   

•  $x-8$  

•  $x+8$  

•  $x-6$  

•  $x+6$  

Finding Solutions

Multiple Choice

f(x)=(x+4)(x-3)(x-2)
List the zeros for this function.

• x= -4, x=3, x= -2
• x= -4, x=3, x=2
• x= -4, x=3, x=2
• x=4, x= -3, x= -2

Multiple Choice

Find all zeros.

• x= 3,1,1/3
• x= -3, -1, -1/3
• x = -3, 1, 1/3
• x = 3, -1, -1/3

Multiple Select

Solve

x³ - 5x² - 4x + 20 = 0 (Make sure to select all the answers that apply)

• 5

• -5

• 2

• -2

• 0

Multiple Choice

How many zeros does the polynomial function
 P(x) = 3x⁴+4x-8 have?

• 1
• 2
• 3
• 4