Factoring and Solving Quadratics

Solving Review

Factoring and Solving Quadratics

We are going to continue reviewing factoring and extend that idea into SOLVING! :)

Multiple Choice

In order to factor the trinomial:  

 $y=x^2+bx+c$   
we need to find to integers that....?

• multiply to b

• multiply to c

• divide by b

• divide by c

Multiple Choice

In order to factor the trinomial:  

 $y=x^2+bx+c$   
we need to find to integers that....?

• add to b

• add to c

• subtract to b

• subtract to c

As an example, if we have x² + 7x + 12

Factors of 12 are: 1 and 12, 2 and 6, 3 and 4, as well as their negatives

  

The only pair that adds up to 7 is 3 and 4.  

This means we can factor it to:   (x+3)(x+4)

  

Multiple Choice

Factor:

 $x^2+9x\ -36$  

• (x + 12)(x  - 3)

• (x + 4)(x + 9)

• (x - 12)(x  - 3)

• (x - 12)(x  + 3)

Multiple Choice

Factor:

 $x^2+5x\ -6$  

• (x + 5)(x  - 6)

• (x + 2)(x + 3)

• (x - 6)(x  - 1)

• (x + 6)(x  - 1)

Multiple Choice

Factor:

 $x^2+7x\ -30$  

• (x + 5)(x  - 6)

• (x + 10)(x + 3)

• (x - 3)(x + 10)

• (x  - 10)(x  - 3)

To solve:

Once you have factored the equation -

Create an equation with each factor

Solve that equation.

(x-4) =0 and (x+5)=0

What would the answers be? Solve for each x

Multiple Choice

Solve for the values of x:

(x - 5)(x - 1) = 0

• x = 5, 1

• x = 5, -1

• x = -5, 1

• x = -5, -1

Multiple Choice

Solve for the values of x:

(x + 2)(x - 3) = 0

• x = 2, 3

• x = -2, -3

• x = 2, 3

• x = -2, 3

Now put it all together

• Factor the trinomial

• Solve each piece for x

Multiple Choice

Solve the equation by factoring:

x² - 6x = -8

• x=2 and x=4

• x= -2 and x= -4

• x= -2 and x=4

• x=2 and x= -4

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

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