Solve Quadratics by Factoring - ZPP Misconception

Solving Quadratics by Factoring Review

Solving quadratics is an important skill that helps us find solutions to hypothetical or real-world problems

There are several methods to solve quadratic equations, today we're reviewing how to solve by factoring!
Some problems are split into multiple questions, so write things down as you go!

​Factored Form

Standard Form

Remember!

Solving using factored form

To solve a quadratic equation by factoring, first you have to have the quadratic expression equal to zero!

When given a problem, this may not be the case so your first step is to set it equal to zero. This may require adding/subtracting a term on both sides.

Then you have to rewrite into factored form and use the zero product property!

Multiple Choice

Is this equation ready to solve by factoring?

$$x^2+2x-8=16$$

• Yes

• No

Open Ended

What do you need to do to in order to make the equation $$x^2+2x-8=16$$ ready to solve by factoring?

Math Response

Once you complete that step, what is the standard form version of the equation?

Type answer here

Correct Answer: x^2+2x-24=0

Deg^°

Rad

Multiple Select

Select the two factors you need for $$x^2+2x-24$$

• (x-4)

• (x+8)

• (x+4)

• (x+6)

• (x-3)

Zero Product Property

Multiple Choice

What are the correct solutions to $$x^2+2x-24=0$$ ?

• x=4, x=6

• x=-4, x=-6

• x=4, x=-6

• x=-4, x=6

• None of these

Now Let's Practice!

Multiple Choice

What is the first step to solve $$x^2+6x-1=-6$$ by factoring?

• Factor the left side

• Add one to both sides

• Add six to both sides

• Use the zero product property

Fill in the Blanks

Write the two solutions, separated by a comma and no space, to the equation $x^2+6x-1=-6$

Multiple Choice

Angelica solved the quadratic equation $$x^2+9x=-20$$ as follows

Step 1: $$x\left(x+9\right)=-20$$

Step 2: $$x=-20$$ or $$x+9=-20$$

Step 3: $$x=-20$$ or $$x=-29$$

Did Angelica solve correctly? If not, what step did she make a mistake?

• She solved correctly

• She made a mistake in Step 1

• She made a mistake in Step 2

• She made a mistake in Step 3

Multiple Select

Select the correct answer(s) to the equation $$x^2+9x=-20$$

• -20

• -29

• 5

• -5

• -4

Multiple Select

Select all the equations that are ready to be solved by factoring

• $$x^2-7=2$$

• $$x^2+4x-60=0$$

• $$x^2=5x-14$$

• $$0=x^2-7x+12$$

• $$x^2-2x+8=-7$$