Math Polynomial Review

Add & Subtract Polynomials

100

Add the Polynomials

(4x + 9) + (x - 4)

5x + 5

200

Add the polynomials:

(-3a - 2) - (7a + 5)

-10a -7

300

Add the polynomials:

(x² +3x + 5) + ( -x² +6x)

9x + 5

400

Add the polynomials:

(t² + 3t³ -3) - (2t² +7t -2t³) 

5t³ - t² -7t -3

500

Add the polynomials: 

(-1 + x² + 2x) + (1 -2x + 2x²)

3x²

600

Add the polynomials:

(-7x⁵ + 14 -2x) + (10x⁴ + 7x + 5x⁵)

-2x⁵ + 10x⁴ +5x + 14

Divide & Subtract Polynomials

100

Divide the polynomials:

(16a² + 4a) / 4a

4a + 1

200

Use synthetic division to evaluate f(-7) if 

f(x) = 4x⁴ + 29x³ + 4x² -14x + 37

f(-7) = -12

300

Divide:

(2x³ - 11x² +13x - 44) / (x - 5)

2x² - x + 8 +  (-4/(9x-5))

400

Divide:

(x³ - 3x² - x - 10) / (x² + 3x - 1)

x - 6 + [(18x - 16)/(x² + 3x - 1)]

500

Subtract the Polynomials:

(2x - 3x) - (x² -2x + 4)

-x² + x - 4

600

Subtract the following polynomials

(3 - 6x⁵ - 8x⁴) - (-6x⁴ - 3x - 8x⁵)

2x⁵ - 2x⁴ + 3x + 3

Review

100

Using two words, name the polynomial.

x²  + 3x - 5

Quadratic trinomial

200

All factors of x³ + 125

What are (x + 5) and (x² - 5x + 25)?

300

The 5 zeros of f(x) = 2x⁵ - 12x³ + 10x

What are 0, -1, 1, -sqrt5, +sqrt5

400

DOUBLE POINTS

End behavior of y = -3x⁵ + 2x - 3

What is

as x->-inf, y->+inf

as x ->+inf, y->-inf

500

DOUBLE POINTS

The equation of a transformed equation when 

f(x) = |x| slides left 3 units, is reflected over x axis and slides up 5 units.

What is g(x) = - |x + 3| + 5 ?

600

DOUBLE POINTS

The solution for 3x⁶ + 12x⁴ = 96x²

What is x = 0,0, -2, 2, -2isqrt2, +2isqrt2

Multiplying Polynomials

100

Multiply the Polynomials:

3x² (2x⁴)

6x⁶

200

Multiply the Polynomials:

3(2x + 4x² - 5)

12x² + 6x - 15

300

Multiply the Polynomials:

(x - 1)(−8x² − 6x − 12 )

-8x³ - 6x² - 12x + 8x² + 6x + 12

-8x³ + 2x² - 6x + 12 (Correct Answer)

400

Multiply the Polynomials:

(x-2)(x+6)

x²+4x-12

500

Multiply the Polynomials:

(3x-6)(5x+3)

15x²-21x-18

600

Multiply the following polynomials

(3r+ 5)²

9r² + 30r + 25

Vocabulary and Rules

100

x²  + 3x - 5

What is a Quadratic trinomials?

200

What is the number that stands alone in an expression called?

What is a Constant?

300

All possible rational roots of f(x) = x³ + 3x² - 6

What are -1, 1, -2, 2, -3, 3, -6, 6?

400

If a function has the zeros x = 4 and x = -3 + sqrt(2), the it must have a third zero.

What is -3 - sqrt(2)?

500

All possible rational roots of f(x) = 2x³ + 3x - 6

What are -1, 1, -2, 2, -3, 3, -6, 6, -1/2, 1/2, -3/2, 3/2?

600

What is the Quadratic Formula?

(-b+-sqrt(b^2-4ac))/(2a)