2/12 - Solve by Factoring

Do Now

7

Factor the following quadratic expressions.

1.

x² - 17x +72

2. 10x² - 22x + 12

LO: SWBAT solve quadratic equations with
real solutions by factoring.

DOL: Given 5 problems, students will
correctly solve quadratic equations with
real solutions by factoring in at least 4 of 5
questions.

ALGI.8A - Solve quadratic equations having real solutions by factoring, taking square roots, completing the square,
and applying the quadratic formula.

8

Lesson Vocabulary

9

Parabola

Axis of
symmetry

x - intercept /
solution / root

y - intercept

Vertex
(max/min)

●Standard Form: y = ax² + bx + c
(general form of a quadratic
function).

●Intercept Form: y = a(x - p)(x-q)
(where the solutions / roots /
intercepts are ).

Lesson Vocabulary

10

Coefficient

Perfect Square

Square Root

3

3

3 x 3 = 9

​7x²

Today you will solve quadratic equations …

by factoring.

11

Let's do a quick review of factoring!

12

13

Recall

Factor out the GCF of 3x³ - 12x2 - 15x.

Image by 巻（Maki） from Pixabay

Steps:

Open Ended

How can you check your work?

Here is the factored form of a quadratic function.

(x - 3)(x + 2)

You have 2 minutes to discuss with your shoulder partner what you notice about the factors in comparison to the zeros of the graph. Use Desmos to see the graph.

16

Solve Quadratic Equations by Factoring

16

The Zero Product Property states that if the product of two or more factors is equal to zero,
then at least one factor must be equal to zero.

You can use the Zero Product Property to identify the zeros of a function when the function is
written in factored form.

Example: Find the solutions of the quadratic equation y = x² – 16
Set the equation equal to 0. 0 = x² – 16

Factor the quadratic equation . 0 = (x + 4)(x – 4)

Set each factor equal to 0.

x + 4 = 0

x – 4 = 0

Solve each equation for x.

x = – 4 x = 4

x = – 4 and x = 4

17

Tech Self check ✔

How can we self
check ✔ our answer?

Use desmos to check your work!

✅

Graph the function y = x² – 16 . Double check that it has
x - intercepts (-4, 0) and (4, 0).

18

Now you try!

18

Solve the quadratic equation y = x² – 9x + 8 by factoring.

Factor the trinomial on your whiteboard. (2 minutes)

Set both factors to zero and solve for x on your whiteboard.
(1 minute)

19

Tech Self check ✔

How can we self
check ✔ our answer?

Use desmos to check your work!

✅

Graph the function y = x² – 9x + 8. Double check that it
has x - intercepts (8, 0) and (1, 0).

20

Continue to Solve Quadratic Equations by Factoring

20

Example: Shakira wrote the quadratic equation 3 = 4x² – 9x + 5. Solve the
equation by factoring.

Multiple Choice

Daniel is solving the quadratic equation 5x² + 11x + 2 = 3x – 1. Which of the
following is a solution to this equation?

• $$x=0$$

• $$x=-1$$

• $$x=3$$

• $$x=\frac{3}{5}$$

Partner Error Analysis (6 minutes)

Work and discuss with your
shoulder partner which student
answered correctly?

Nina

Wendy

Nina and Wendy are debating who found the solutions to g(x) = 0, when the function g(x) = 2x2 + 15x – 8.

22

→g(x) = 2x2 + 15x – 8

→0 = 2x2 + 15x – 8
→0 = (2x – 1)(x + 8)

→(2x – 1) = 0 (x + 8) = 0

→x = x = – 8

→g(x) = 2x2 + 15x – 8

→0 = 2x2 + 15x – 8
→0 = (2x + 1)(x – 8)

→(2x + 1) = 0 (x – 8) = 0

→x = x = 8

Math Response

Mrs. Johnson just purchased a new poster for her classroom. The length of a rectangular poster is 5 more feet than two times its width. The area of the
poster is 52 square feet.

$$52=2x^2+5x$$

Solve for the width of the poster.

Type answer here

Correct Answer: 4

Deg^°

Rad

Demonstration of Learning

DOL:Given 5
problems, students
will correctly solve
quadratic equations
with real solutions
by factoring in at
least 4 of 5
questions.

29

Open Ended

How do you solve quadratic equations by
factoring?

Use complete sentences: To solve a quadratic equation by factoring...