Download Use the distributive property to factor each polynomial

Use the distributive property to factor each polynomial.
12mn + 80m2
Find the GCF for each term:
12mn = 2  2  3  m  n
80 m2 = 2  2  2  2  5  m  m
So GCF = 4m
Write each term as the product of the GCF and its
remaining factors.
12mn + 80m2 = 4m(3n) + 4m(2  2  5  m)
= 4m(3n) + 4m(20m)
= 4m(3n + 20m)
Check your answer by doing distributive
Try again:
14c3 – 42c5 – 49c4
14c3 = 2  7  c  c  c
42c5 = 2  3  7  c  c  c  c  c
49c4 = 7  7  c  c  c  c
So GCF = 7c3 … take 7c3 “out” of each term
14c3 = 7c3 (2)
42c5 = 7c3(6c2)
49c4 = 7c3(7c)
7c3(2 – 6c – 7c)
Check your answer by distributing!
Factor by grouping:
6ax + 3ay + 2bx + by
= (6ax + 3ay) + (2bx + by)
= 3a(2x + y) + b(2x + y)
parenthesis should turn out to be identical
= (3a + b)(2x + y)
Check by using the FOIL method!!
Try again:
6xy – 8x + 15y – 20
= (6xy – 8x) + (15y – 20)
= 2x(3y – 4) + 5(3y – 4)
= (2x + 5)(3y – 4)
You could also regroup the terms
differently!!
TRY  (6xy + 15y) + (-8x – 20)
= 3y(2x + 5) + -4(2x + 5)
= (3y + -4)(2x + 5) or (3y – 4)(2x + 5)
Check by using the FOIL method!!
Solve equation by factoring:
9x2 + x = 0
factor out the GCF
x(9x + 1) = 0
use the zero product property
x=0
or
9x + 1 = 0
9x = -1
x = -1/9
check your answers, plug them in
Try some more:
(r – 3)(r + 2) = 0 use the zero product property
r – 3 = 0 or r + 2 = 0
r=3
or
r = -2
x2 = -3x
move -3x over to left  x2 + 3x = 0
factor out x  x(x + 3) = 0 use zero product prop.
x = 0 or
x+3=0
x = -3
check your answers, plug them in
Solve equation by factoring:
9x2 + x = 0
factor out the GCF
x(9x + 1) = 0
use the zero product property
x=0
or
9x + 1 = 0
9x = -1
x = -1/9
check your answers, plug them in
Try some more:
(r – 3)(r + 2) = 0 use the zero product property
r – 3 = 0 or r + 2 = 0
r=3
or
r = -2
x2 = -3x
move -3x over to left  x2 + 3x = 0
factor out x  x(x + 3) = 0 use zero product prop.
x = 0 or
x+3=0
x = -3
check your answers, plug them in