6.1 Factoring Polynomials
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Transcript of 6.1 Factoring Polynomials
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 Factor
s
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 remainder97 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 remainder3 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 remainder3 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
Is 291 divisible by 4?
91 4 leaves a remainder4 is a not a factor of 291
4 if the number formed by the last two digits is divisible by 4
Divisible by…2 if last digit is an even number.
3 if the sum of the digits is divisible by 3
Is 932 divisible by 4?
32 4 leaves no remainder4 is a factor of 932
4 if the number formed by the last two digits is divisible by 4
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 Factoring Polynomials”Polynomials”
the REVERSE of the Distributive Property
Factor: 10x + 15
5
What # or variable is a factor of both terms? 5
2x
5
+ 3
Check your answer!!!!!
Factor: 12x + 4
4
What # or variable is a factor of both terms? 4
3x
4
+ 1
Check your answer!!!!!
Factor: 18x3 + 12x
6 x
6x
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
5xy3(x4y + 4)
5 x y3 ( )
35xy 35xy
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