Solving Quadratics by Zero Product Property

Solving Quadratics by Factoring

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Solving Quadratics by Factoring

We will be combining the zero product property and the factoring methods we learned in the last unit to solve quadratic equations.

Every problem will follow the steps on the next slide. I will include videos and more detailed examples for each factoring method throughout.

Grab a piece of paper to take notes and write down examples!

For every problem, follow these steps. Write them down!!!

• 1. Make sure the equation is equal to zero.

• 2. Factor the left side of the equation (using one of these methods we learned in the last unit: trinomials where a=1, GCF, difference of squares, or trinomials where a>1). This one is a trinomial where a=1, so we just needed to find what multiplied to -8 and added to -2.

• 3. Set each factor equal to zero and solve for x. (This is what you practiced yesterday!)

Trinomial where a=1

Copy and paste this link to watch some examples:

https://www.youtube.com/watch?v=rYlr7oXl8AQ

Multiple Choice

Solve by factoring: x² + 3x - 18 = 0

• x = -3 and x = 6
• x = 3 and x = -6
• x = -9 and x = 2
• x = 9 and x = -2

Multiple Choice

Solve by factoring: x² - 9x + 20 = 0

• x = -4 and x = -5
• x = 20 and x = -9
• x = 4 and x = 5
• x = -4 and x = 5

Trinomial where a>1

Copy and paste the link to watch some examples:

https://www.youtube.com/watch?v=b3slW0UhQ0Q

For this one, notice the equations are not already equal to zero, so she has to make sure to do that first!

Multiple Choice

Solve by factoring: 2x²+ 7x + 6 = 0

• x= 3/2 and x = 2

• x = -3/2 and x = -2

• x = 6 and x = 7

• x = -6 and x = -7

Multiple Choice

What should you do first in solving this equation?

x² + 6x - 13 = 3

• Get factored form

• Write down: a=1, b=6, c=-13

• Make it equal 0 by subtracting 3 on each side

• Type it all in a calculator.

Multiple Choice

$$x^2\ +\ 5x\ =\ -6$$  

Set the equation equal to zero.

• $$x^2+5x-6=0$$  

• $$x^2+5x+6=0$$

• $$x^2=-5x\ -6$$

GCF Only

Copy and paste the link to watch some examples:

https://www.youtube.com/watch?v=gIwMkTAclw8

Multiple Choice

Solve for x: 3x² - 9x = 0

• x = 3

• x = 0, 3

• x = -3, 9

• x = 9

Difference of Squares

Copy and paste the link to watch some examples:

https://www.youtube.com/watch?v=PNFMcIhG-CM

Multiple Choice

Solve

16a² - 9 = 0

• a = ^-3/₄, ³/₄

• a = ^-4/₃, ⁴/₃

• a = ^-9/₁₆, ⁹/₁₆

• a = ^-16/₉, ¹⁶/₉