Question

Part A: Factor 5x2b^2 + 14xb^2 − 3b^2. Show your work. (4 points)

Part B: Factor x^2 − 18x + 81. Show your work. (3 points)

Part C: Factor x^2 − 121. Show your work. (3 points)

Answer 1

A.
alright
we can factor out the b² from everybody

b²(5x²+14x-3)
use ac method
for ax²+bx+c
multiply ac, and remember te result
find what 2 numbers multiply to ac and add to get b
split b up into those 2 numbers
factor
it's confusing so see example below
so

b²(5x²+14x-3)
5 times -3=-15
what 2 numbers multiply to get -15 and add to get 14?
15 and -1
b²(5x+15x-1x-3)
group
b²((5x²+15x)+(-1x-3))
b²(5x(x+3)-1(x+3))
factor
b²(5x-1)(x+3)



B.
what 2 numbers multiply to get 81 and add to get -18?
-9 and -9
(x-9)(x-9) or
(x-9)²

C.
diff of 2 perfect squares
remember a²-b²=(a+b)(a-b)
so
x²-11²=(x+11)(x-11)