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6.1 Factoring Polynomials
• Goal: To factor out a common factor of a
polynomial
Factoring (Divide):
Convert a number or expression into
an equivalent expression that is the
product of two or more expressions.
6  2  3 12  4  3
12  6  2
12  3  2  2
PRIME
Factors
Relatively prime
• No common factors
Example:
4 and 7
Divisible by…
2 if last digit is an even number.
3 if the sum of the digits is divisible
by 3
4 if the number formed by the last
two digits is divisible by 4
5 if the number ends in 0 or 5
7 Nike Rule: “just do it” (long division)
9 if the sum of the digits  by 9
10 if the last digit is a zero.
Divisible by…
2 if last digit is an even number.
3 if the sum of the digits is divisible
by 3
Is 97 divisible by 3?
9  7  16 16  3 leaves a remainder
97 is not divisible by 3
Divisible by…
2 if last digit is an even number.
3 if the sum of the digits is divisible
by 3
Is 105 divisible by 3?
1  0  5  6 6  3 leaves no remainder
3 is a factor of 105
Divisible by…
2 if last digit is an even number.
3 if the sum of the digits is divisible
by 3
Is 291 divisible by 3?
2  9 1  12 12  3 leaves no remainder
3 is a factor of 291
Divisible by…
2 if last digit is an even number.
3 if the sum of the digits is divisible
by 3
4 if the number formed by the last
two digits is divisible by 4
Is 291 divisible by 4?
91  4 leaves a remainder
4 is a not a factor of 291
Divisible by…
2 if last digit is an even number.
3 if the sum of the digits is divisible
by 3
4 if the number formed by the last
two digits is divisible by 4
Is 932 divisible by 4?
32  4 leaves no remainder
4 is a factor of 932
Is 9,365,126,210 divisible by 4?
10  4 leaves a remainder
4 is not a factor of
9,365,126,210
Is 3,228 divisible by 4?
28  4 = 7 with no remainder
4 is a factor of 3,228
5(x + 3) = 5x + 15
“Factoring
Polynomials”
the REVERSE of the Distributive
Property
Factor: 10x + 15
5
5  2x
5
+3
What # or
variable is a
factor of both
terms?

Check your answer!!!!!
What # or
variable is a
factor of both
terms?
Factor: 12x + 4
4
4  3x
4
+1

Check your answer!!!!!
Factor:
3
18x
+ 12x
6x
6 x  3x2
6x
+2

Check your answer!!!!!
Factor x2 + 7x
x • x + x •7
x(x + 7)
Factor a2b + 2ab
a•a • b + 2 • a • b
a(ab + 2b)
ab(a + 2)
Factor 5x5y4 + 20xy3
3
3
5xy
5xy
5 x y3 ( x4y + 4
5xy3(x4y + 4)
)
Factor 16y5 + 20y3
4y3(4y2 + 5)
Factor
x3(9 + 25x4)
Factor
3m3n(4m2n + 3m + 2n)
Factor
16x(x5 - 2x4 - 3)
Factor
x2(6x2 - 10x + 3)
Factor
2a2(2a2b4 – ab2 + 6)
Which polynomial has 3x as a factor?
Homework
Page 264 ( 10-50) even