Transcript Factoring Binomials ax2 + bx +c

Factoring Trinomials 9-4
2
ax
+ bx +c
Chapter 9
Check to see if there are any
common factors.
2
2x
+ 22x + 36
2 is a common
factor
2
2x
+ 22x + 36
Factor
out a 2
2
2(x + 11x + 18)
Hint: Divide each number by 2
2
2(x
+ 11x + 18)
Now factor
2
(x
+ 11x + 18)
Hint: Look at the signs. Will
you be adding or
subtracting?
2
(x
+ 11x + 18)
(x + )(x + )
Hint: Start by finding the
factors of x.
2
(x
+ 11x + 18)
(x + )(x + )
Find the factors of 18
that will add to get
11.
2
(x
+ 11x + 18)
The factors of 18 are
1,2,3,6,9,18
2 and 9 add to be 11
2
(x
+ 11x + 18)
(x + 2)(x + 9)
Is the answer for
2
(x
+ 11x + 18)
The final answer is
Now put it all together
2(x + 2)(x + 9)
Add the 2 we
factored out to the
answer.
Prime Polynomial
A polynomial that can not
be written as a product
of two polynomials with
integral coefficients.
Example
2
8b
-5b -10 multiply the a and c
8 * -10 = -80
Factors of -80 would be
1, -80
8, -10
2, -40
4, -20 No factors have a sum of -5
2
7x
+ 22x +3
a = 7, b = 22, c = 3
We need to find two numbers
whose sum = 22 and whose
product = 7 * 3 = 21.
Make a list of the factors of 21
7x2 + 22x +3
21
1, 21
Sum
22
so m = 1 and n = 21
Now put these factors into the
2
pattern ax + mx + nx + c
7x2 + x + 21x + 3
2
7x

+ x + 21x + 3
Group terms with common factors
(7x2 + x) + (21x + 3)
x(7x + 1) + 3(7x + 1)
(x + 3)(7x + 1) the answer