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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)