Topic 3 - Polynomial Review

Add/Subtract

100

(5x²+4x)+(9x²-5+3x)

14x²+7x-5

200

(6x²+7x-2)+(1-5x³+3x)

-5x³+6x²+10x-1

300

(5x²+4x)-(9x²-5+3x)

-4x²+x+5

400

(5x-2x²)-(4x²+6x-9)

-6x²-x+9

500

(5x²+7x+2)-(3x²-9x)

2x²+16x+2

Multiply

100

5x²(3x-2)

15x³-10x²

200

-3x(2x²-6x+1)

-6x³+18x²-3x

300

(x-2)(x²-2x-3)

x³-4x²+x+6

400

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

4x²-25

500

(x-3)³

x³-9x²+27x-27

Factor

100

15x²y-10xy²

5xy(3x-2y)

200

9x²-25

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

300

10x²-19x-15

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

400

6x³+3x²+2x+2

(x+1)(3x²+2)

500

3x³+24

3(x+2)(x²-2x+4)

Divide

100

(x²-7x-11)÷(x-8)

x+1 R: -3

200

(3x³-11x²+7x-3)÷(x-3)

3x²-2x+1

300

(x²-28)÷(x-5)

x+5 R:-3

400

(8x⁴-6x²-2x+4)÷(2x-1)

4x³+2x²+4x+1 R:5

500

(x³-1)÷(x-2)

x²+2x+4 R:7

Polynomial Fun

100

List all possible rational roots of f(x)=2x³+3x²-5x+4

±1, ±2, ±4, ±0.5

200

Given f(x)=3x⁵-2x⁴+5x³-x²+4x+1, find f(1).

10

300

If -2 is a zero of f(x)=x³+kx²+5x-6, what is the value of k?

k=6

400

Let P(x) be a cubic polynomial with no constant term and a root at 1+i. Find a possible expression for P(x).

P(x)=x³-2x²+2x

500

P(x)=a₃x³+a₂x²+a₁x+a₀ has a root at -1. If the sum of the roots is 6 and the product of the roots is 8, find the other two roots.

-1 and 8