Factoring Binomials

Algebra Lesson 9-5

Let’s Review

1) 6ab + 3a

2) 5x3 – 3y2

3) 2c4 – 4c3 + 6c2

4) 4w4n + 12w4n+3

Your Turn to Try!

1) 6ab + 18a2

2) 5x3 + 10x2 – 20x

3) 2x2 – 3y2

4) 3w2n + 21w2n+2

Factoring PolynomialsFind the common binomial factor, then rewrite the distributive property.

r(t + 1) + s(t + 1) = (r + s)(t + 1)

Example Problems

1) a(x – 3) + 6(x – 3)

2) a(b + 4) + c(b + 4)

3) x(y + 1) – 2(y + 1)

4) m(n2 + 3) + 4(n2 + 3)

5) p(2q + 5) – (2q + 5)

Factoring the expression

ab + 4a + cb + 4c

• Group the terms that have a common number or variable as a factor.

• Factor the GCF from each group.

• Regroup the expression.

Reteaching the Lesson

x2 + 7xy + 9xy + 63y2

Reteaching the Lesson

m2n + mn – 4m – 4

Factor Practice

1) 6a + 18 + ba + 3b

2) xy – x – 3y + 3

3) 2mn + 4n – m – 2

4) p2q – p2 + 4q – 4

Answers

1) 6(a + 3) + b(a + 3)

2) x(y – 1) – 3(y – 1)

3) 2n(m + 2) – (m + 2)

4) p2(q – 1) + 4(q – 1)

Classwork

• Text pg. 450 & 451# 22 – 32 & #50 – 54 (Even)

• Text pg. 451# 55 – 58 (ALL)

Factoring PolynomialsRegrouping is another way to factor polynomials. Look and group terms that have common number or variable as a factor. Then factor the GCF from each group. Rewrite terms using distributive property.

x2 + x + 2x + 2 = (x2 + x) (2x + 2)

x(x + 1)= + 2(x + 1)

= (x+2)(x+1)

Extra Practice Problems

1) ax + bx + ay + by

2) mn + mp + 5n + 5p

3) 4ax – bx + 4ay – by

4) 3a + 3 – a2 – a

5) 3m – 12 + m3 – 4m2

Your Turn to Try!

1) xy + 2y + x + 2

2) 2xz + 2yz + x + y

3) 2cd – c – 6d + 3

4) 12ab – 15a – 8b +10

5) x2 + 3x + 4x + 12

Practice Problems

1) 2pq2 + 4pq – 2q – 4

2) 6m3 + 4m – 9m2 – 6

3) ab2 + 5a – 6b2 – 30

4) 4 – 2x + 6 – 3x

5) mx + 5m + nx + 5n

6) 3x2 + 3xy – 2xy – 2y2

Warm Up

Find the GCF of each set of numbers. 1. 6, 152. 16, 24, 603. 3, 6, 14, 28 Multiply. 4. 4(h2 – 5)5. 2b(b2 – 9b)

Factoring PolynomialsFind the GCF of the terms, then rewrite the distributive property.

5am – 5an = 5a (m – n)

Extra Practice Problems

1) 4y3 – 16y4

2) 6p + 15p2 – 9pq

3) 8r4 + 17s4

4) 7m3n + 21m3n+1

Let’s Review

Factor.

• 24x3 + 8x7

• 5y3 + 15y2

• 3ab2 + ab

• 2m2 + 2m + 4m3

Warm Up

Factor. 1. 3k2 + 212. 2y2 – 15y3. 6c3 + 9c2

4. 12x3y – 14x2y2

5. 15p2q3 + 20p5q4 – 25p2q2

Classwork

• Text pg. 450 # 13 – 42 (ALL)