Factoring Review

Factoring Quadratics Review

Multiple Choice

Factor the following trinomial:

 $x^2-10x+24$  

•  $\left(x+6\right)\left(x-4\right)$  

•  $\left(x-6\right)\left(x+4\right)$  

•  $\left(x-6\right)\left(x-4\right)$  

•  $\left(x+6\right)\left(x+4\right)$  

Quadratic

• a quadratic is a type of polynomial

• polynomials are expressions made up of terms being added together like x + 5 or x³ - 6x + 1

• a polynomial is a quadratic if the highest exponent of a variable is 2

Multiple Choice

Is the following a quadratic expression?  $x^3+x^2+5$  

• Yes

• No

Multiple Choice

Is the following a quadratic expression?  $x^2+3x+2$  

• Yes

• No

Multiple Choice

Is the following a quadratic expression?  $5x+x^2+1$  

• Yes

• No

Multiple Choice

Which is NOT a quadratic expression?

• $x^2+4x$

• $x^2+5x-6x^7$

• $4-x^2$

• $x\cdot x$

We use a, b, and c to describe a quadratic

• a: coefficient of x² term

• b: coefficient of x term

• c: constant (number without variable)

Fill in the Blanks

Identify C

10x² + 7x - 20

Fill in the Blanks

Identify A

x² + 4x + 5

Fill in the Blanks

Identify B

4x + x² + 3

Fill in the Blanks

Identify C

3x² - 8x

Factoring Quadratics

• to factor a quadratic, we start by identifying two numbers that multiply to ac and add up to b

• a = 1 , b = 3 , c = 2

• ac = 1(2) = 2

• b = 3

Factoring Quadratics

• to factor a quadratic, we start by identifying two numbers that multiply to ac and add up to b

• What two numbers multiply to 2 AND add up to 3?

Factoring Quadratics

•  $1\cdot2=2$  
  

•  $1+2=3$  

Factoring Quadratics

• Identify ac and b

• ac = 2( -3) =- 6

• b = -5

Factoring Quadratics

• What are two numbers that multiply to -6 AND add up to -5 ?

Factoring Quadratics

•  $-6\cdot1=-6$  
  

•  $-6+1=-5$  

Fill in the Blanks

Identify ac from the quadratic x²-2x + 1

Fill in the Blanks

What two numbers multiply to ac = 1 and add up to b = -2 ?

x²-2x+1

Type answers as # and #

Fill in the Blanks

Identify ac from the quadratic 3x² + 13x + 4

Fill in the Blanks

What two numbers multiply to ac = 12 and add up to b = 13?

3x² + 13x + 4

Fill in the Blanks

Identify ac from the quadratic x²+4x-12

Fill in the Blanks

What are two numbers that multiply to ac = -12 and add up to b = 4?

x²+4x-12

Fill in the Blanks

Identify ac from the quadratic 6x²-10x - 4

Fill in the Blanks

What are two numbers that multiply to ac = -24 and add up to b = -10 ?

6x²-10x - 4

Fill in the Blanks

Identify ac of the quadratic -9x + x² + 8

Fill in the Blanks

What two numbers multiply to ac = 8 and add up to b = -9? -9x + x²+8

Fill in the Blanks

Identify ac of the quadratic 2x² - 8

Fill in the Blanks

Identify b of the quadratic 2x² - 8

Fill in the Blanks

What are two numbers that multiply to ac = -16 and add up to b = 0 ?

2x² - 8