Chapter 6 Summative Review

Factoring a=1

100

Factor: x²-3x-28

(x-7)(x+4)

200

Factor: x²+5x-36

(x-4)(x+9)

300

Factor: x²+15x+56

(x+7)(x+8)

400

Factor: x²+13x-30

(x-2)(x+15)

500

Factor: x²+18x+32

(x+16)(x+2)

Factoring a>1

100

Factor: 5x²-12x+7

(x-1)(5x-7)

200

Factor: 3x²+8x+4

(x+2)(3x+2)

300

Factor: 6x²-43x+7

(6x-1)(x-7)

400

Factor: 2x²-13x+21

(2x-7)(x-3)

500

Factor: 16x²+13x-3

(16x-3)(x+1)

Factoring with a GCF

100

Factor: 3x²+33x+90

3(x+5)(x+6)

200

Factor: 6x²+39x-21

3(x+7)(2x-1)

300

Factor:10x²-38x+24

2(x-3)(5x-4)

400

Factor:4x³+36x²+56x

4x(x+7)(x+2)

500

Factor: 6x³+14x²-12x

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

Special Cases

100

Factor: x³+216

State the identity.

(x+6)(x²-6x+36)

Sum of two cubes

200

Factor: 16x⁴-9

State the identity.

(4x²-3)(4x²+3)

Difference of two squares

300

Factor: 3x³-75x

State the identity.

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

Difference of two squares

400

Factor: 128x³-250

State the identity.

2(8x-5)(64x²+40x+25)

Difference of two cubes

500

Factor: x⁶+64y⁶

State the identity.

(x²+4y²)(x⁴-4x²y²+16y⁴)

Sum of two cubes

Pythagorean Triples

100

List the most commonly known Pythagorean triple.

3, 4, 5

200

Verify that the group 20, 21, 29 is a Pythagorean triple.

(20²)+(21²)=(29²)

400+441=841

841=841

300

Generate a Pythagorean triple using the following values:

x=8, y=5

39, 80, 89

400

Generate a Pythagorean triple using the following values:

x=17, y=9

208, 306, 370

500

Generate a Pythagorean triple using the following values:

x=43, y=22

1365, 1892, 2333