2.3 - Factoring Polynomials PDF

Preview

Summary

help you improve your skills in math, specifically in functions and factoring polynomials...

Description

2.3 Factoring Polynomials

Date:

2.3 – Factoring Polynomials Factoring a polynomial means writing it as a product. So factoring is the opposite of expanding. Factoring

x 2 + 3x − 4 = (x + 4)(x − 1) Expanding To factor polynomials fully, you can use factoring strategies that include: 1.

Always look for any GREATEST COMMON FACTORS (GCF):

Example: Factor the following: a)

4 x 4 − 8x 3 + 2x 2

2.

Recognizing a SIMPLE TRINOMIAL:

b)

2 x 2 y 2 − 8x2 y + 10 xy2

ax2 − bx + c where a = 1

Example: Factor each of the following: a)

3.

x 2 + 7 x + 12

Recognizing COMPLEX TRINOMIALS:

b)

x 2 − 2x − 8

ax 2 + bx + c where a  1

Example: Factor each of the following (using decomposition): a)

2 y 2 + 11y + 12

b)

6 x 2 − 13x + 6

MCR 3U1 – Homework: Page 102 #1, 2c, 3 – 6, 7bc, 8, 9df, 10, 11, 15a

Page 1

2.3 Factoring Polynomials

Date:

2 2 Recognizing a DIFFERENCE OF SQUARES: ( a − b ) = ( a − b)( a + b)

4.

Example: Factor each of the following: a)

( x2 − y2 )

5.

b)

4 − 81y 2

Recognizing a PERFECT SQUARE TRINOMIAL: 2

a + 2ab + b2 = (a + b)2 and a2 − 2 ab + b2 = ( a − b)2 Example: Factor each of the following: 2

a) 9 x + 30 x + 25

6.

b)

x 2 −10 x + 25

Factoring by GROUPING: If a polynomial has more than three terms, you may be able to factor it by grouping. This is only possible if the grouping of terms allows you to divide out the same common factor from each group.

Example: Factor each of the following: a)

ax + ay + bx + by

b)

x3 + x2 + x + 1

MCR 3U1 – Homework: Page 102 #1, 2c, 3 – 6, 7bc, 8, 9df, 10, 11, 15a

Page 2

2.3 Factoring Polynomials

Example 1:

Date:

Factor fully.

a) x2 + 5x + 6

b) x2 + 5x – 84

c) 2m2 + 7m + 3

d) 3x2 + 16xy + 5y2

e) 3(x-y)2 + 2x2 – 2xy

f) 3(2x-5y)2 + 6x2 + 9xy – 60y2

MCR 3U1 – Homework: Page 102 #1, 2c, 3 – 6, 7bc, 8, 9df, 10, 11, 15a

Page 3...