Chapter 11

Degree & Standard

100

Standard form of 4 - x² + 2x

-x² + 2x + 4

200

Degree of (x² + 1)(x² - 1)

4

300

Degree of x³(x² - x⁴ + 1)

7

400

Is x(x + 1/x) a polynomial?

Yes (it simplifies to x² + 1)

500

Degree of 5 + 0x⁴ - x²

2

Sum & Difference

100

(x² + 5) + (2x² - 3)

3x² + 2

200

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

-2x - 10

300

(x² - 4x) + (2x² + 4x - 7)

3x² - 7

400

(2x² - x) - 3(x² + x)

-x² - 4x

500

Add x² - 1 to x - x² + 4

x + 3

Product Peak

100

2x(3x² - x + 4)

6x³ - 2x² + 8x

200

(x - 6)(x + 4)

x² - 2x - 24

300

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

6x² + 11x - 10

400

(x + 3)(x² - 3x + 9)

x³ + 27

500

(3x - 1)(x² + 2x - 4)

3x³ + 5x² - 14x + 4

Special Identities

100

Factor x² - 64

(x + 8)(x - 8)

200

Expand (x + 9)²

x² + 18x + 81

300

Factor 25x² - 4

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

400

Expand (2x - 7)²

4x² - 28x + 49

500

Factor 81x² - 100y²

(9x + 10y)(9x - 10y)

Factoring Stretches

100

Factor x² - 9x + 20

(x - 4)(x - 5)

200

Factor x² + 3x - 28

(x + 7)(x - 4)

300

Factor x² + 2x + 5

Prime

400

Factor 2x² + 11x + 5

(2x + 1)(x + 5)

500

Factor 6x² + 7x - 3

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