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

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