Polynomials and Factoring

Simplifying Polynomials

100

(5x² + 4x - 2) + (3x² + 7)

8x² + 4x + 5

200

(4x⁴ - 3x² - 1) + (3x⁴ + 6x²)

7x⁴ + 3x² - 1

300

(3x³ - 2x) - (8x³ + 4x)

-5x³ - 6x

400

(7x⁴ + 3x³ - 5x + 1) - (x³ + 8x² - 5x - 3)

7x⁴ + 2x³ - 8x² + 4

500

(ab² + ba³) - (4a³b - ab² - 5ab)

2ab² - 3a³b + 5ab

Distributive Property

100

10a(-6a² + 2a - 7)

-60a³ + 20a² - 70a

200

t²(t + 1) - t(2t² - 1)

-t² + t² + t

300

(u - 6)²

u² - 12u + 36 

400

(3w + 7)(2w² - 5)

6w³ +14w² - 15w - 35

500

(z + 4)(z - 4)(z + 8)

z³ + 8z² - 16z - 128

Factor polynomials

100

6x - 4

2(3x - 2)

200

10t³ - 20t² + 35t

5t(2t² - 4t + 7)

300

x² - 17x + 60

(x - 12)(x - 5)

400

8x² + 18x + 9 

(2x + 3)(4x + 3)

500

12x² - 41x + 35

(4x - 7)(3x - 5)

Finding Roots/zeros

100

(x + 8)(x - 5) = 0

-8 and 5

200

x(x - 6)(x + 13) = 0

0, 6, and -13

300

x² + 7x - 18 = 0

(x + 9)(x - 2) ---> -9 and 2

400

2g² - 35g + 17

(2g - 1)(g - 17) ---> 1/2 and 17

500

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(2m +  1)(2m - 1)(2m + 3) ---> 1/2, -1/2, and -3/2

Miscellaneous

100

x² + 5x - 10

trinomial

200

8x²

monomial

300

Name the polynomial

2x + 1

binomial

400

Factor completely

5g⁴ - 5g³ + 20g² - 20g

5g(g² + 4)(g - 1)

500

Factor by grouping

y³ + 11y² - 4y - 44

(y + 2)(y - 2)(y + 11)