7.1-7.6 Review: Factor Polynomials

Classify

100

Name the polynomial

8

Constant Monomial

200

Name the polynomial

7x²-5x+9

quadratic trinomial

300

Name the polynomial

3x³-6

Cubic Binomial

400

2x²+7y+3x⁵+9

5th degree polynomial

Quintic Polynomial

500

Name the polynomial

2x-16

Linear Binomial

Factor by Grouping

100

3x^2-11x+10

(x-2)(3x-5)

200

9m^2+3m-2

(3m+2)(3m-1)

300

x^3+x^2+2x+2

(x^2+2)(x+1)

400

x^3+4x^2+2x+8

(x^2+2)(x+4)

500

9x^2-3xy+6x-2y

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

Multiplying Polynomials

100

Multiply the Polynomials:

3x² (2x⁴)

6x⁶

200

Multiply the Polynomials:

(x - 3)(x + 2)

x² - x - 6

300

Multiply the Polynomials:

(2x-6)²

4x² -24x +36

400

Multiply the Polynomials:

(4n - 1)(3n + 4)

12n² + 13n - 4

500

Multiply the Polynomials:

(d + 3)(d² - 4d + 1)

d³ - d² -11d + 3

Factoring GCF

100

Factor out the GCF

30x-42

6(5x-7)

200

Factor out the GCF

5a³+2a² - 3a

a(5a² + 2a - 3)

300

Factor out the GCF

24x⁴y + 6x³y² - 18x²y³

6x²y(4x² + xy - 3y²)

400

Factor out the GCF

15mn³ - 8mn + 2n² - 10m³

The polynomial is completely factored

500

Factor out the GCF

18n⁴+42nm+6n

6n(3n^3+7m+1)

Factor Special Cases

100

Factor:

x² - 16

(x + 4)(x - 4)

200

Factor

x² - 22x + 121

(x - 11)²

300

Factor:

x² + 18x + 81

(x + 9)²

400

Factor:

4p² - 256

4(p+8)(p-8)

500

Factor:

5x³ + 30x² + 45x

5x(x + 3)²

Factoring a=1

100

Factor:

p² +12p +35

(p+5)(p+7)

200

Factor:

x² + 7x - 30

(x - 3)(x + 10)

300

Factor:

2x² - 10x - 12

2(x + 1)(x - 6)

400

Factor:

x⁴ + 3x²y⁴ + 2y⁸

(x² + y⁴)(x² + 2y⁴)

500

Factor:

8m³n² + 8m²n³ - 48mn⁴

8mn²(m + 3n)(m - 2n)

Factoring a>1

100

Factor:

2x² + x - 10

(2x - 5)(x + 2)

200

Factor:

10x² + 3x - 4

(5x + 4)(2x - 1)

300

Factor:

30x² - 68x + 32

2(5x - 8)(3x - 2)

400

Factor:

12x⁵ +26x⁴ - 10x³

2x³(2x + 5)(3x - 1)

500

Factor:

x³ + x² - x - 30

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