4.2 and 4.3 Review

Adding and Subtracting Polynomials

100

(-4x^2-6x+18)+(-x^2+7x+8)

-5x^2+x+26

200

(48+6x^2-12x)-(-x^2+24x-63)

7x^2-36x+111

300

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

2x^3+6x^2-3x-1

400

(-11x^4-x^3-3x^2+10x-2)-(-11x^4+5x^2-7x+13)

-x^3-8x^2+17x-15

500

(xy^2+a-b-x^2y)-(5xy^2-3a+b+3x^2y)

-4xy^2-4x^2y+4a-2b

Multiplying Polynomials

100

(x-5)(x+3)

x^2-2x-15

200

(4x-3)(2x+7)

8x^2+22x-21

300

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

9x^2-25

400

(3x+1)(x^2+8x+7)

3x^3+25x^2+29x+7

500

(2x-5)^4

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

Long Division

100

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

2x^-3x+5+(-4x-11)/(x^2+3x+2)

200

(X^3-x^2-2x+8)/(x-1)

x^2-2+(6/(x-1))

300

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

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

400

(x^2+x-17)/(x-4)

x+5+(3/(x-4))

500

(3x^2-14x-5)/(x-5)

3x+1

Synthetic Division

100

(-x^3+4x^2+9)/(x-3)

-x^2+x+3+(18/(x-3))

200

(x^3-x^2-9x+18)/(x+3)

x^2-5x+6

300

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

3x^2-5x+7-(12/(x+1))

400

Evaluate the function using Synthetic Division

f(x) = 5x^3-x^2+13x+29 

when x=-4

f(-4)=-359

500

Evaluate the function using synthetic division

f(x) = 5x^4+2x^3-20x-6

when x=2

f(2)=50

Vocab and Core Concepts

100

What are like terms?

Terms with same variables and exponents

200

What is a binomial?

An expression with 2 terms.

300

What is a linear factor?

A factor with the highest degree of 1 written in the form (x-k)

400

What is Pascal's Triangle?

A shortcut method to multiply polynomials with binomial expansion.

500

What is the perfect cube pattern?

a^3+3a^2b+3ab^2+b^3