Topic 7: Polynomials

Multiply Polynomials

100

Multiply the binomials: 

(x + 3)(x + 2).

x²+5x+6

200

Multiply: 

(2x + 1)(x − 4).

2x²-7x-4

300

Multiply a trinomial by a binomial: 

(x² + x + 2)(x + 3)

x³+4x²+5x+6

400

Multiply: 

(2x + 3)(x² − x + 4).

2x³+x²+5x+12

500

Multiply: 

(3x2− 2x + 1)(2x + 5).

6x³+11x²-8x+5

Factoring GCF

100

Factor out the greatest common factor: 6x + 9

3(2x+3)

200

Factor: 12x² − 8x.

4x(3x-2)

300

Factor out the GCF: 15x3 + 10x²− 5x.

5x(3x²+2x−1)

400

Factor the GCF from 18x²y − 12xy² + 6xy.

6xy(3x−2y+1)

500

Factor the GCF from: 24x³ − 36x²+ 12

12x(2x²−3x+1)

Grouping

100

Factor by grouping

x³ + x² + x + 1.

(x²+1)(x+1)

200

Factor by grouping: 

3x³ + 6x² + 2x + 4.

(3x²+2)(x+2)

300

Factor by grouping: x³ − 2x² + 3x − 6

(x²+3)(x−2)

400

Daily Double!

(2x+1)(x²−4)

BONUS: (2x+1)(x−2)(x+2)

500

Factor by grouping 

x³ + 2x + 4x² + 8.

(x+4)(x² +2)

Factoring Trinomials

100

Factor the trinomial: x²+ 5x + 6.  

(x+2)(x+3)

200

Factor: x² − x − 12.

(x−4)(x+3)

300

 Factor: 2x² + 7x + 3

(2x+1)(x+3)

400

x² + 2x + 7.

Not factorable

500

Factor 3x² − 14x + 8.

(3x−2)(x−4)

Special Cases

100

Factor: x²− 9

(x−3)(x+3)

200

Factor x² + 6x + 9 

(x+3)2²

300

Factor: 4x² + 12x + 9.

(2x+3)²

400

Factor the binomial: 16x² − 25.

(4x−5)(4x+5)

500

Factor 9x⁴ − 6x² + 1.

(3x²−1)²