6.3 solving by factoring

6.3 Solving Quadratic Equations by Factoring

What is Factoring?Used to write trinomials as a product of binomials.

Works like FOIL in reverse.Example: Multiply (x + 2)(x + 7)

What do you notice about the 2 and 7?

Factoring x2 + bx + c x2 + bx + c = (x + m)(x + n) Need to find m and n so

m+n = b and m·n = cFirst, find all factor pairs of c.Find their sums. Choose the pair whose sum

equals b.

Example:Factor x2 + 5x + 6

Multiply (FOIL) to check your answers!

Factor Pairs Sum

Example:Factor x2 + 13x + 40 Factor

Pairs Sum

You Try!Factor x2 + 9x + 14

More FactoringWhat if b is negative and c is

positive?For example: x2 - 7x + 10

◦Choose negative factors!

You Try!Factor x2 - 4x + 3

What if?What if c is negative?For example: x2 - 8x – 20

◦Choose one positive and one negative!

Example:Factor x2 + 3x – 10

You Try!Factor x2 - 2x – 48

Factoring Out MonomialsCheck if you can factor out

something from each term.Example: Factor 5x2 – 15x – 20

Example:Factor 2x2 + 8x

You Try!Factor: 6x2 + 15x 4x2 - 20x

+24

Solving by FactoringSome quadratic equations can

be solved by factoring.Standard form: ax2 + bx + c = 0

Zero Product Property:◦If A x B = 0, then A = 0 or B = 0.

So, to solve:Get equation equal to zeroFactor completelySet each factor equal to zeroSolve for xExample: Solve x2 + 3x – 18 =

0

Examples:Solve by factoring.x2 - 3x – 4 = 0

x2 - x - 2 = 4

You Try!Solve by factoring.x2 + 19x + 88 = 0

Examples:Solve by factoring:2x2 + 8x – 64 = 0

-3x2 + 36x - 72 = 36

You Try!Solve by factoring.-4x2 - 4x + 48 = 0

Applications – Area Problems1. Draw a picture!2. Write an equation.3. Get eqn. into standard form.4. Factor.5. Solve.6. Answer the question with a

SENTENCE.

Example 1:A square field had 5m added to its

length and 2m added to its width. The new area is 150m2. Find the length of a side of the original square.

x

x

+5

+2

Example 2:A rectangular garden is 3m long by

10m wide. You want to increase the length and the width by the same amount to double the area. Find the dimensions of the new garden.

10

3

+ x

+ x

You Try!A rectangular garden is 4m long by

5m wide. Each dimension is increased by the same amount. The new area is 56m2. Find the dimensions of the new garden.