Algebra II: Polynomial Operations and Factoring

Add, Subtract, Multiply

100

(4x^2−3x+5)+(x^2+7x−2)

5x^2+4x+3

200

(x^3−6x+10)−(2x^3+x^2−5)

−x^3−x^2−6x+15

300

2x(3x^2−5x+4)

6x^3−10x^2+8x

400

(x^2+2)(x^2−3x+1)

x^4−3x^3+3x^2−6x+2

500

(2x+5)^4

16x^4 + 160x^3 + 600x^2 + 1000x + 625

Division 1

100

(x²-3x-40)/ (x+5)

x-8

200

(x³+3x²-x+2)/(x-1)

x^2+4x+3 + 5/(x-1)

300

(x³+27) / (x+3)

x²-3x+9

400

(x⁴+3x³+x+4) / (x+3)

x^3-3x^2+12x-35 + 109/(x+3)

500

(x⁵+1) / (x+1)

x⁴-x³+x²-x+1

Division 2

100

Divide the polynomial

(3x^2+7x-20) / (3x+4)

x+3-32/(3x+4)

200

Divide the polynomial

(2x^2+x-7) / (2x+11)

x-5 +48/(2x+11)

300

Divide the polynomial

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

3x+4 + (5x+1)/(x^2-x-1)

400

Divide the polynomial

(x^4+5x^3-x^2-2x+1) / (x^2+2x-1)

x^2+3x-6 + (16x-5)/(x^2+2x-1)

500

Divide the polynomial

(x^3-3x^2+4x-10) / (x^2+4)

x-3 + 11/(x^2+4)

Factoring 1

100

Factor the polynomial:

x³+7x²+10x 

x(x+5)(x+2)

200

Factor the polynomial:

9x³+6x²-3x

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

300

Factor the polynomial :

8x^3-125

(2x-5)(4x^2+10x+25)

400

factor the polynomial:

x^3 -5x^2-x+5

(x − 5)(x + 1)(x − 1)

500

Factor the polynomial:

x ^6 − 26x^3 − 27

(x − 3)(x^2 + 3x + 9)(x + 1)(x^2 − x + 1)

Factoring 2

100

5x^4+29x^2+20

(5x^2+4)(x^2+5)

200

x^4-2x^2-15

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

300

x^4-4x^2-45

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

400

x^6+2x^4-16x^2-32

(x^2+2)(x^2+4)(x+2)(x-2)

500

x^9-x^6-x^3+1

(x-1)^2(x^2+x+1)^2(x+1)(x^2-x+1)