FACTORING DIFFERENT TYPES OF POLYNOMIALS Common Monomial

FACTORING DIFFERENT TYPES OF POLYNOMIALS

Common Monomial Factors

Sum and Difference of two Squares

Sum and Difference of Two Cubes

Perfect Square Trinomials

General Trinomials

Quarter1_Week1_Module1

Factoring by Grouping

ac + ad + bc + bd = (a + b)(c + d)

Grouping means isolating terms using parenthesis( )

• Example: ab + ac + mb + mc can be grouped into:

• (ab + ac) + (mb + mc)

• What is common to the first group? a

• What is common to the second group? m

• Hence, we can factor them in this manner: a(b + c) + m(b + c)

• What is common to both groups? (b + c)

Factoring by Grouping

• EXAMPLE NO. ! Factor: ab + ac + mb + mc

• Step no.1 Group the terms. (ab + ac) + (mb + mc)

• Step 2: Get the CMF or common monomial factor in each group

• Step 3: Factor this out: a(b + c) + m(b + c)

• Step 4: Get the common binomial factor.and factor this out.

• Hence, ab + ac + mb + mc= (b + c)(a + m)

Examples:

Ex.1. Factor: 2x + 2y + ax + ay

Solution: (2x + 2y) + (ax + ay) = 2(x + y) + a(x + y)

.............................................................. = (x + y)(2 + a)

Ex. 2. Factor completely: 4ab³ - abc² + 5b² - 5c²

Solution: (4ab³ - abc² )+ (8b² - 2c²) = ab(4b²- c²) + 2(4b² - c²)

..........................................................................=(4b²- c²)(ab + 2)

......................................................................... = (2b + c)(2b - c)(ab + 2)

Multiple Choice

What is the best groupings of the terms in the polynomial:

3x + 3y + bx + by

• (3x + 3y) + (bx + by)

• (3x + 3y)(bx + by)

• (3x + by) + (3y + bx)

• (3x - by) + (3y - bx)

Multiple Choice

What monomial is common to both terms: 10mn - 10mp?

• 10

• m

• 10m

• np

Multiple Choice

The common binomial factor in 3ax - 3ay + bx - by is:

• x - y

• x + y

• 3a + b

• 3a - b

Multiple Choice

The common binomial factor in 7a(m + n) - b(m + n) is:

• 7a - b

• m + n

• m - n

• 7b

Multiple Choice

Factor completely: 8x³ - 2xy² + 20x² - 5y²

• (x²- y²)(2x + 5)

• (4x²- y²)(2x + 5)

• (2x + y)(2x - y)(2x + 5)

• (4x²- y²)(2x - 5)

Multiple Choice

Factor: 6xy - 6xz + 7my - 7mz

• (6xy - 6xz)(7my - 7mz)

• (y - z)(6x + 7m)

• (6 - my)(7 + xz)

• (6 + my)(7 + xz)

Multiple Choice

Factor completely: 2a + 3bm + 2m + 3ab

• (a + m)(2 + 3b)

• (a + 2)(m + 3b)

• (a + 3b)(2 + m)

• (a + 3b)(2 - m)

Multiple Choice

Group the terms in this expression: 2a + 3bm + 2m + 3ab

• (2a + 2m) + (3bm + 3ab)

• (2a + 2m) + (3ab + 3bm)

• (2a + 3bm) + (2m + 3ab)

• (2a - 3bm) + (2m + 3ab)

Multiple Choice

Factor : 9x + 9y + mx + my

• 9(x + y)

• m(x + y)

• (x + y)(9 + m)

• (x - y)(9 + m)

Multiple Choice

What binomial is common in the following expression?

a(5 - y) + b(5 - y)?

• (a + b)

• (5 - y)

• a(5 - y)

• a(5 + y)

Congratulations!

• Study well!

• Keep on going....