Topic 6: Polynomials and Factoring

Adding and Subtracting Polynomials

100

(2x+4)+(5x+7)=

7x+11

200

(3x⁴ + 2 − 2x³) + (4x³ + 4x⁴)=

7x⁴+2x³+2

300

(4x³ + 6x – 7) + (3x³ – 5x² – 5x)=

7x³-5x²+x-7

400

(−5x + 4) − (3x² − 7x + 4)=

-3x²+2x

500

(4y + 5y² − 6) − (5y + 27 − y²)=

6y²-y-33

Multiplying Polynomials

100

Find the product. (x+4)(x+3)

x²+7x+12

200

Find the product. (3x+7)(2x+4)

6x²+26x+28

300

2x²(−2x³ + x − 3).

-4x⁵+2x³-6x²

400

Find the product. x² – 4x + 4 and 6x + 3?

6x³+21x²+12x+12

500

Find the product of (3x³ − 2)(4x⁴ − 3x + 8).

12x⁷−17x⁴+24x³+6x−16

Dividing Polynomials/ GCF

100

Find the GCF of 6x³ and 24x².

6x²

200

What is 24x²-16x+20 divided by 4?

6x²-4x+5

300

The quotient of 30y³+50y²-35y divided by 5y is

6y²+10y-7

400

Factor out the GCF from the terms of the polynomial 2x³ − 5x² + 25.

The polynomial is already fully factored.

500

Factor out the GCF from the terms of the polynomial −2x⁵ − 6x³ − 16x².

−2x²(x² + 3x + 8)

Factoring Trinomials (a=1)

100

What is the factored form of y² + 11y + 28?

(y+4)(y+7)

200

What is the factored form of x² + 7xy + 10y²?  

(x+5y)(x+2y)

300

What is the factored form of x² − 9x + 20?

(x − 4)(x − 5)

400

What is the factored form of y² + 6y − 16?

(y + 8)(y − 2)

500

What is the factored form of x² + 4xy − 21y²?

(x − 3y)(x + 7y)

Factoring Trinomials (a>1)

100

What is the factored form of 2x² + 10x + 12?

2(x+2)(x+3)

200

Factor the perfect square trinomial 25x² – 60x + 36.

(5x – 6)²

300

What is the factored form of 6x² + 17x + 5?

(2x+5)(3x+1)

400

What is the factored form of 2x² + 5x − 12?

(2x − 3)(x + 4)

500

What is the factored form of 2x² − 7x − 15?

(2x + 3)(x − 5)