8.2 Multiplying and Factoring

Subtracting Polynomials

100

(x+5)-(3x-10)

-2x+15

200

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

-x^2-x-5

300

(2x^2-4x)-(x^2-8x+7)

x^2+4x-7

400

(-5x^3+x^2)-(-6x^3-12x^2+14)

x^3+13x^2-14

500

(5x^3+13x^5-3x^2+7)-(-x^4+16x^5-x)

-3x^5+x^4+5x^3-3x^2+x+7

Adding Polynomials

100

(x^2+7x)+(-3x^2+5x)

-2x^2+12x

200

(4xy-7x)+(xy+3x)

(5xy-4x)

300

(6d^4+4d)+(3d^4-d^2-d)

9d^4-d^2+3d

400

(x^2-8x+16)+(x^2+6x+9)

(2x^2-2x+25)

500

(3z^5-4z^2+7)+(8z^4-6z^5+2z^2)

-3z^5+8z^4-2z^2+7

Determining GCF of Polynomials

100

The greatest common factor of this polynomial:

2x+16

2

200

The greatest common factor of this polynomial:

b^3+3b^2-b

b

300

The greatest common factor of this polynomial:

21f^4-99f^3+18f^2

3f^2

400

The greatest common factor of this polynomial:

13xy^2+17x^4y^17-5x^3y^6

xy^2

500

The Greatest Common Factor of this polynomial

6xyz^3-72xz^2+552xz

6xz

Multiplying Polynomials by Monomials

100

x^2(x+18)

x^3+18x^2

200

-2b(b^3+4b-7)

-2b^4-8b^2+14b

300

wr(-7+r)

wr^2-7wr

400

-3yz(y^2-14y+49)

-3y^3z+42y^2z-147yz

500

5d^3f^2h(7h^2df^5-3d^3+5fh-2)

35h^3d^4f^7-15d^6f^2h+25d^3f^3h^2-10d^3f^2h

Factoring Polynomials by GCF

100

2x^3-4x^2+3x

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

200

-w^3+15w^2

-w^2(w-15)

300

-2b^3+22b^2-2b

2b(-b^2+11b-1)

400

-72x^3y^2+81x^2y

9x^2y(-8xy+9)

500

The result of factoring a monomial out of this polynomial:

54r^6h^3-6h^2r^3+12hr^2

6r^2h(9r^4h^2-hr+2)