Ch. 5 Review

Polynomials

100

State the degree and Leading coefficient:

12x²-5x⁴+6x⁸-3x-3

8 and 6

200

Find P(-2)

P(x)=3x² - x

14

300

Find P(x+h)

P(x)=3x² - x

3x²+6xh+3h²-x-h

400

Factor:

a⁴-16

(a-2)(a+2)(a²+4)

500

Factor:

6ay + 4by - 2cy + 3az + 2bz - cz

(2y+z)(3a+2b-c)

Solve

100

Solve:

x³+2x²-35x=0

-7,0,5

200

Solve:

8x⁴-10x²+3=0

+- Sqrt(3)/2, +- Sqrt(2)/2

300

Solve:

4x³+4x²-x-1=0

-1, -1/2, 1/2

400

Solve:

x³+4x²-11x-30=0

3, -2, 5

500

Solve:

x³+2x²+4x+8=0

-2, 2i, -2i

Theroems

100

Find f(-2) by synthetic substitution:

f(x)=x²-5x+4

18

200

Find f(4) by synthetic substitution:

f(x)=2x⁴-3x³+1

321

300

State the number of possible zeros:

f(x)= -2x³+11x²-3x+2

3

400

State the number of possible turning points:

f(x)= x⁶-5x³+x²+x-6

5

500

State all possible rational zeros:

f(x)= x³+4x²-11x-30

+- 1, 2, 3, 5, 6, 10, 15, 30

Simplify

100

Simplify:

3t(tn-5)

3t²n-15t

200

(x⁴)³

x¹²

300

3b(2b-1) + 2b(b+3)

8b²+3b

400

(-4a³b⁵)(5ab³)

-20a⁴b⁸

500

(2x²+3x-8)+(3x²-5x-7)

5x²-2x-15

Division

100

Divide:

(12x⁴y⁵+8x³y⁷-16x²y⁶) / 4xy⁵

3x³+2x²y²-4xy

200

Divide:

6y³+13y²- 10y-24 /  (y+2)

6y²+y-12

300

Divide:

4a⁶-5a⁴+3a²-a / (2a+1)

2a⁵-a⁴-2a³+a²+a-1 R:1

400

Divide:

6x³-31x²-34x+22 / (2x-1)

3x²-14x-24 R: -2

500

Divide:

3x³+11x²-114x-80 / (3x+2)

x²+3x-40