Objective # 16
Factoring Polynomials - 1st Step: Factor Out Common Factors
Material:
page 134 to 140
Homework: worksheet
are expressions that are being added or subtracted
Terms
Examples:
3x3y2z
3x + 4y
x2 - 3x + 5
one term
two terms
three terms
monomial
binomial
trinomial
are expressions that are being multiplied
Factors
Examples:
Factoring
(3)(4)
two factors
(5)(x + 3)
two factors
(4x)(x - 2)
two factors
(x - 1)(2x + 3) two factors
3 and 4
5 and x + 3
4x and x - 2
x - 1 and 2x + 3
is a process used to find all the factors that were multiplied to give a polynomial expression.
Three methods for factoring polynomials:
1st
Factor out common factors
2nd
Factor the binomial called the difference of two squares into the product of its conjugate pairs.
3rd
Factor trinomials into the product of two binomials.
Example 1:
Multiple each of the following factors:
a)
(3)(x + 2)
b)
(-2)(5x - 1)
c)
- (4 - x2)
d)
(x)(x + 3)
e)
(3x)(4 - 2x)
f)
(-5x)(2x - 3)
g)
(x)(x2 + 4x - 3)
h)
(2x)(1 + 5x - 3x3)
i)
(-4x2)(3x -2)
Example 2:
Factor out the common factors (if any) in each of the following polynomials:
a)
3x + 9
b)
12x - 16
c)
24 + 16x - 8x2
d)
x2 + 4x
e)
3x3 - x2
f)
5x + 3x2 + 2x3
g)
4x2 + 12x
h)
8x3 - 28x
i)
15x3 + 6x2 - 9x
Factoring Polynomials - 1st Step: Factor Out Common Factors
Worksheet
1.
Multiple each of the following factors:
a)
-(x - 1)
b)
(4)(7x - 2)
c)
(-3)(2x2 + 5x -1)
d)
(x)(2x + 3)
e)
(7x)(x - 2)
f)
(-2x)(4x2 - 3x + 9)
g)
(x2)(1 - 2x)
h)
(5x3)(3 + 2x)
i)
(-x2)(2 - x + 3x2)
j)
(3x)(4 - 2x2)
k)
(-x)(-5x - 2)
l)
-(3x2 + 7x - 4)
2.
Factor out the common factors (if any) in each of the following polynomials:
a)
7x - 14
b)
10 - 15x
c)
24x2 + 36x - 12
d)
2x2 - 3x
e)
x3 + x 2
f)
2x3 - x2 + 5x
g)
12x + 8
h)
5x2 - 20x
i)
2x3 + 6x2 - 8x
j)
6x2 + 15
k)
4x3 - 9x2
l)
9x3 - 15x2 + 21x
m)
18x4 + 27x2
n)
4x4 + 6x3 - 8x2 + 10x
o)
18x - 12x2
p)
(3x)(x + 4) + (2)(x + 4)
q)
(2x)(3x - 1) - (5)(3x - 1)
r)
(x)(2x + 1) + (2x +1)