Factoring Polynomials Factoring Polynomials Factoring Polynomials.

Factoring PolynomialsFactoring Polynomials Factoring PolynomialsFactoring Polynomials

Example 1

Find factorizations of 6x2.

(1)(6x2)

(2)(3x2) (6)(x2) (1x)(6x)

(2x)(3x)

(-1)(-6x2)

(-2)(-3x2) (-3)(-2x2)

Example 2Factor.

a) 5x3 + 10

5( )

x3 + 2

b) 6x3 + 12x2

6x2( )x + 2

c) 12u3v2 + 16uv4

4uv2( )

3u2+ 4v2

PracticeFactor.

1) x2 + 3x

2) a2b + 2ab

Example 3Factor.

d) 18y4 – 6y3 + 12y2

e) 8x4y3 – 6x2y4

f) 5x3y4 + 7x2z3 + 3y2z

Example 3Factor.

d) 18y4 – 6y3 + 12y2

6y2( )3y2 - y

e) 8x4y3 – 6x2y4 2x2y3( )4x2 - 3y

f) 5x3y4 + 7x2z3 + 3y2z

+ 2

No common factors

PracticeFactor.

1) 3x6 – 5x3 + 2x2

2) 9x4 – 15x3 + 3x2

PracticeFactor.

3) 2p3q2 + p2q + pq4) 12m4n4 + 3m3n2 + 6m2n2

Factor by Grouping• When polynomials contain four terms,

it is sometimes easier to group like terms in order to factor.

• Your goal is to create a common factor.• You can also move terms around in the

polynomial to create a common factor.• Practice makes you better in

recognizing common factors.

Factoring Four Term Factoring Four Term PolynomialsPolynomials

Factoring Four Term Factoring Four Term PolynomialsPolynomials

Factor by Grouping

• FACTOR: 3xy - 21y + 5x – 35• Factor the first two terms: 3xy - 21y = 3y (x – 7)• Factor the last two terms: + 5x - 35 = 5 (x – 7)• The green parentheses are the same so

it’s the common factor

Now you have a common factor (x - 7) (3y + 5)

Factor by Grouping

• FACTOR: 6mx – 4m + 3rx – 2r• Factor the first two terms: 6mx – 4m = 2m (3x - 2)• Factor the last two terms: + 3rx – 2r = r (3x - 2)• The green parentheses are the same so

it’s the common factor Now you have a common factor

(3x - 2) (2m + r)

Factor by Grouping• FACTOR: 15x – 3xy + 4y –20• Factor the first two terms: 15x – 3xy = 3x (5 – y)• Factor the last two terms: + 4y –20 = 4 (y – 5)• The green parentheses are opposites so

change the sign on the 4 - 4 (-y + 5) or – 4 (5 - y)• Now you have a common factor (5 – y) (3x – 4)