Factoring Trinomials
Hints to remember to solve these: 1. TAKE YOUR TIME, be sure to pay attention to all negative signs! 2. Write these notes down!
Review:
(x + 2)(x + 5) 2 x + 2x + 5x + 10 2 x + 7x + 10
Today we are going to do this BACKWARDS… We are going to FIND THE FACTORS of a Trinomial.
Just like multiplying polynomials, this takes practice…
Trog says “TAKE YOUR TIME!!!”
Before you start, be sure the trinomial is in order, with the HIGHEST EXPONENT written first.
+ 4x - 6 + 3x
2
How to Factor a Trinomial MATH
STEPS
x + 7x + 10
1. Put a 1 in front of any letters and turn any minus signs to adding a negative.
1x + 7x + 10
2. Multiply the FIRST number times the LAST number, write the answer to the side and circle it.
2
2
This number is SPECIAL!
1x2 + 7x + 10 10
1x2 + 7x + 10
10
?•? 1x2 + 2x + 5x +10
3. Now figure out factors of the special number that add up to the middle number. 4. Once you figure out the two factors, split up the middle term using those two numbers.
1x2 + 2x + 5x +10
5. Group the first two and the last two terms.
1x ( 2 + 2x)+ (5x +10)
6. Now factor each group.
x(x +2) + 5(x + 2)
…almost there…..!!!
x (x + 2) + 5 (x + 2)
( x + 5 ) (x + 2)
FACTORED!
7. UNDISTRIBUTE the groups. 8. Group up the remaining factors.
Don’t Freak Out! Like anything else, it takes practice & patience!