Polynomials & Factoring Review

Adding/Subtracting Polynomials

100

Add the following polynomials

x⁴+4x⁴

5x^4

200

Subtract the following polynomials

7x⁴-2x⁴

5x^4

300

Add the following polynomials

(3x³+x²+9)+(x³-3x²+1)

4x^3-2x^2+10

400

Subtract the following polynomials

(5a³ - 2a²) - (4a³+3a²)

a³ - 5a²

500

Add the following polynomials

(2k³-7k)+(-5k³-k²-3k)

-3k^3-k^2-10k

Multiplying Polynomials

100

Multiply the following polynomials

w²(w²+3)

w^4+3w

200

Multiply the following polynomials 

r²(7r³-3r+9)

7r^5-3r^3+9r^2

300

Multiply the following polynomials

(9m-3)(2m+3)

18m^2+21m-9

400

Multiply the following polynomials

(3r²+5)²

9r^4+30r^2+25

500

Multiply the following polynomials

(t²+4)(t³+6r-3)

t^5+6t^2r-3t^2+4t^3+24r-12

Factoring Polynomials

100

Factor the polynomial

15g³-5g

5g(3g^2-1)

200

Factor the polynomial

3g⁵+9g³-18g²

3g^2(g^3+3g-6)

300

Factor the polynomial 

16x²-4

4(4x^2-1)

400

Factor the polynomial

x²+5x-14

(x-2)(x+7)

500

Factor the polynomial

4x²+22x+10

2(2x^2+11x+5)

or 2(x+5)(2x+1)

General Polynomials

100

The degree of this polynomial: 

x³-7x²+4x⁵-19x⁷

7

200

Classify this polynomial:

2x³+3x-7

Cubic Trinomial 

300

Classify:

10

Constant Monomial 

400

True or False

Polynomials can have constants, variables and exponents

True

500

The degree of this polynomial

6x³-3x+12x⁵+x⁴

5

More Factoring Polynomials

100

What is the GCF of 12x² and 3x?   

3x

200

Factor out the GCF:

10x⁵ + 40x²

5x²(2x³+ 8)

300

Factor the trinomial: x² + 8x + 15

(x + 5)(x + 3)

400

Factor the trinomial: 2x² + 11x + 5

(2x + 1)(x + 5)

500

Factor out the GCF, then factor the trinomial:

3x³ + 21x² + 30x

3x(x+ 5)(x + 2)