Solving Equations by Factoring

Expanding BinomialsFactoring

(x+3)(2x-1)

(3x-1)(x-2)

Don't worry about moving slowly, worry about standing still. -- Chinese proverb

Quotable

Solidify factoring in terms of solving equations.

Objective

Zero Product Property

If a = 0 or b = 0 then ab = 0

You can use this property to solve certain equations!

SOLVE(x+2)(x-5) =0

Since the answer is zero, you know that one of the factors has got to equal zero.

Set each equal to zerox+2=0 x-5=0x=-2 x=5

Therefore the solution set is {-2,5}, x is either equal to -2 or 5.

5n(n-3)(n-4)=0

Again, you know one of the factors must equal zero so set them all to zero.

5n =0 n-3= 0 n-4=0n=0 n=3 n=4

The solution set is {0, 3, 4}

Solve

Polynomial Equation- an equation whose sides are both polynomials

Linear equation-> ax+b=0

Quadratic equation-> ax² + bx +c

Cubic equation-> ax³ + bx² + cx + d

Vocabulary

2x² + 5x = 12

1. Transform into standard form1. 2x² +5x -12 = 0

2. Factor the left side1. (2x-3)(x+4)=0

3. Set each factor equal to zero and solve.1. 2x-3 = 0 x+4 = 02. x=3/2 x=-4

4. Check your solutions

Solve

18y³ +8y +24y²=0

1. Transform into standard form1. 18y³ + 24y² + 8y= 0

2. Factor completely1. 2y(9y²+ 12y+4)2. 2y(3y+2)²

3. Set each part equal to zero1. 2y=0; y=02. (3y+2)²; y=-2/3

4. CHECK!

Solve

Page 232; 1-12

Class Exercises

Pg. 232; 1,7,13,19,25, and 31

Homework