Solving Quadratics by Factoring

Solving Quadratics by Factoring

Multiple Select

Which of the following mean the same thing as "roots?"

• x-intercepts

• zeros

• y-intercepts

• solutions

Multiple Choice

Factor:

x² + 11x + 24

• (x + 6)(x + 4)

• (x + 12)(x + 2)

• (x - 8)(x - 3)

• (x + 8)(x + 3)

Open Ended

Here is the graph of $y=x^2+11x+24$ .

In factored form, it was 
 $y=\left(x+3\right)\left(x+8\right)$ .

What do you notice about the factors compared to the x-intercepts of the equation?

Multiple Choice

What are the factors of 3x²-17x+10

• (x-5)(3x-2)
• (x+5)(3x+2)
• (3x-5)(x-2)
• (x+5)(3x-2)

Open Ended

Here is the graph of $y=3x^2-17x+10$ .

In factored form, it was y=(3x-2)(x-5)

What do you notice about the factors compared to the zeros of the graph?

Multiple Choice

Find the factors of 5x²+20x+20

• 5(x+2)(x+2)
• 5(x-2)(x-2)
• 5(x+2)(x-2)
• (5x+2)(x+2)

Open Ended

Here is the graph of $y=5x^2+20x+20$ .

In factored form, it was  $y=5(x+2)^2$ .

What do you noticed about the factors compared to the zeros of the graph?

Zero Product Property

https://www.youtube.com/watch?v=HpWQh3MSpKk

Steps to Solve a Quadratic Equation by Factoring:

• Make sure the equation is in standard form

• Change the y to 0

• Factor

• Use the zero product property to solve (i.e. set each factor equal to zero and solve for the variable)

Multiple Choice

What is the first step in solving 
(x + 2)(x - 3) = 0      ?

• Plug in zero for x
• Solve for x
• FOIL
• Set each binomial factor equal to zero

Multiple Choice

Solve for the values of x:
(x - 3)(x + 6) = 0

• { -3, -6 }
• { 3, -6 }
• { -3, -6 }
• { 3, 6 }

Multiple Choice

Factor Completely: 
3x² + 18x +15
Hint: Factor GCF first.

• 3(x² + 6x + 5)
• (x + 5)(x + 1)
• 3(x + 5)(x + 1)
• Prime

Multiple Choice

Solve:

3x² + 18x +15 = 0

Hint: Factor GCF first.

• x = 3, 2

• x = 5, 1

• x = -5, -1

• x = -3, -2

Multiple Choice

Solve:

x² +0x - 49 = 0

• x = -7, x = 7

• x = -7

• x = 7

• x = -7, x = 1

Multiple Choice

Solve:  $2x^2-15=x$  

•  $x=-\frac{5}{2}$  and  $x=3$  

•  $x=\frac{5}{2}$  and  $x=-3$  

•  $x=\frac{5}{2}$  and  $x=3$  

•  $x=-\frac{5}{2}$  and  $x=-3$  

Multiple Choice

What are the values of x when y = 0?

• { -3, 1 }
• { -2 }
• { -3, -1 }
• { 1, 3 }

Multiple Choice

Solve:

k² - 2k = 24

• k = -4, 6

• k = -4, -6

• k = -6, 1

• k = 4, -6