10.4

Factoring to solve Quadratics

10.4 – Factoring to solve Quad.

Goals / “I can…”Solve quadratic equations by factoring

10.4 – Factoring to solve Quad.

So far we’ve found 2 ways to solve quadratic functionsGraphingSquare Roots

y = x2 – 4x – 5

Solutions are

-1 and 5

10.4 – Factoring to solve Quad.

Solve 4z2 = 9.

SOLUTION

4z2 = 9 Write original equation.

z2 = 94

Divide each side by 4.

Take square roots of each side.z = ± 94

z = ± 32

Simplify.

10.4 – Factoring to solve Quad.

Example 1Example 2

x2 = 49 (x + 3)2 = 25

x = ± 7 x + 3 = ± 5 x + 3 = 5 x + 3 = –5

x = 2 x = –8

2 49x 2( 3) 25x

Example 3

x2 – 5x + 11 = 0

This equation isnot written in thecorrect form to use this method.

10.4 – Factoring to solve Quad.

10.4 – Factoring to solve Quad.

If I have 2 numbers and multiply them together, and the product is zero, what are the two numbers?

10.4 – Factoring to solve Quad.

One of them must be zero.

10.4 – Factoring to solve Quad.

Zero Product Property – For every real number a and b, if ab = 0

then a = 0 or b = 0.

10.4 – Factoring to solve Quad.

So if I have

(x + 4)(x + 5) = 0

then either

(x+ 4) = 0

or

(x + 5) = 0

Example 1

x2 – 2x – 24 = 0

(x + 4)(x – 6) = 0

x + 4 = 0 x – 6 = 0

x = –4 x = 6

Example 2

x2 – 8x + 11 = 0

x2 – 8x + 11 is prime; therefore, another method must be used to solve this equation.

10.4 – Factoring to solve Quad.

10.4 – Factoring to solve Quad.

Example:Given the equation, find the solutions

(zeros)

(x + 7)(x – 4) = 0(2x + 3)(6x – 8) = 0

10.4 – Factoring to solve Quad.

So, if you have a trinomial equal to zero, you can factor it to find the zeros.

10.4 – Factoring to solve Quad.

Example:

x + x – 42 = 0 3x – 2x = 21

2 2

10.4 – Factoring to solve Quad.

Story Problem:Suppose that a box has a base with a

width of x, a length of x + 2 and a height of 3. It is cut from a square sheet of material with an area of 130 in . Find the dimensions of the box.

2

10.4 – Factoring to solve Quad.

What we have is this:

3

3

x + 2

x