Polynomial Functions

Factor

100

9x³+18x

9x(x²+2)

200

5x²+19x-4

(5x-1)(x+4)

300

8x³+24x²+5x+15

(8x²+5)(x+3)

400

4xy+3+12x+y

(4x+1)(y+3)

500

27x⁴-8x

x(3x-2)(9x²+6x+4)

Factor & Solve

100

x³-x=0

x=0

x=1

x=-1

200

x⁴+4x²+3=0

x=i √ 3

x=-i √ 3

x=i

x=-i

300

x⁴-9x²+18=0

x=√ 6

x=-√ 6

x=√ 3

x=-√ 3

400

x³+27=0

x=-3

x=(3+3i√ 3)/2

x=(3-3i√ 3)/2

500

x⁵-x²=0

x=0, mult. of 2

x=1

x=(-1+i√ 3)/2

x=(-1-i√ 3)/2

Polynomial Division

100

Divide using synthetic division.

(x³-x²-63x-47)/(x+7)

x²-8x-7 + (2)/(x+7)

200

Divide using synthetic division.

(-41n+7n²+3n³-5)/(n+5)

3n²-8n-1

300

Divide using synthetic division.

(b⁴+10b³+31b²+36b+15)/(b+3)

b³+7b²+10b+6 + (-3)/(b+3)

400

Divide using long division.

(-9k-59k²+17+45k³)/(5k-6)

9k²-k-3 + (-1)/(5k-6)

500

Divide using long division.

(50x³+80x²-10x-42)/(5x+5)

10x²+6x-8 + (-2)/(5x+5)

Rational Root Theorem

100

List the possible rational roots.

f(x)=5x³+17x²+26x+8

All plus or minus:

1, 2, 4, 8, 1/5, 2/5, 4/5, 8/5

200

Find all real roots.

f(x)=x³-x²-5x-3

x=3

x=-1, mult. of 2

300

Find all real roots.

f(x)=x³+9x²-21x+11

x=-11

x=1, mult. of 2

400

Find all real roots.

f(x)=2x³-3x²-9x+14

x=2

x=(-1+√ 57)/4

x=(-1-√ 57)/4

500

Use the calculator to find all roots.

f(x)=2x³-25x²+38x+30

x=5/2

x=5+√ 31

x=5-√ 31

Evaluating

100

Evaluate the following function at a=5

f(a)=-3a⁴+9a³+32a²-15a+16

f(5)=-9

200

Evaluate the following function for a=-2

f(x)=-4a⁴-7a³-a²-4a-7

f(-2)=-11

300

Evaluate the following function at a=-3

f(x)=a³+a²+25

f(-3)=7

400

Evaluate the following function at a=-5

f(x)=5a³+30a²+21a-24

f(-5)=-4

500

Evaluate the following function at a=3.

f(x)=6a³-22a²+11a-7

f(3)=-10