Question

review
simplify the following expressions.

1. (x+1)(x+3) 2) (x-4)(x+10) 3) (3x-2)(x-6)

trinomial factoring
example 1:
x² + 5x + 6
2+3 1*6
2*3
-1*-6
-2*-3
(x+2)(x+3)
example 2:
x² - 1x - 6
2-3 -1*6
-2*3
1*-6
2*-3
(x+2)(x-3)
steps:

1. find all factors of c
2. find the pair of

factors of c that add to
equal b

1. put those numbers in

parenthesis with the
variable.
factor the following expressions using trinomial \abc\ factoring.

1. x² + 4x + 4 5) x² - 9x + 20 6) x² + 4x - 12

Explanation:

Step1: Expand using FOIL method

$(x+1)(x+3) = x^2 + 3x + x + 3$

Step2: Combine like terms

$x^2 + (3x+x) + 3 = x^2 + 4x + 3$

Step1: Expand using FOIL method

$(x-4)(x+10) = x^2 + 10x - 4x - 40$

Step2: Combine like terms

$x^2 + (10x-4x) - 40 = x^2 + 6x - 40$

Step1: Expand using FOIL method

$(3x-2)(x-6) = 3x^2 - 18x - 2x + 12$

Step2: Combine like terms

$3x^2 + (-18x-2x) + 12 = 3x^2 - 20x + 12$

Step1: Find factors of 4 that sum to 4

Factors of 4: $2*2$, and $2+2=4$

Step2: Write factored form

$(x+2)(x+2) = (x+2)^2$

Step1: Find factors of 20 that sum to -9

Factors of 20: $(-4)*(-5)$, and $-4+(-5)=-9$

Step2: Write factored form

$(x-4)(x-5)$

Step1: Find factors of -12 that sum to 4

Factors of -12: $6*(-2)$, and $6+(-2)=4$

Step2: Write factored form

$(x+6)(x-2)$

Answer:

1. $\boldsymbol{x^2 + 4x + 3}$
2. $\boldsymbol{x^2 + 6x - 40}$
3. $\boldsymbol{3x^2 - 20x + 12}$
4. $\boldsymbol{(x+2)^2}$
5. $\boldsymbol{(x-4)(x-5)}$
6. $\boldsymbol{(x+6)(x-2)}$