Question

Explain, in complete sentences, how you would completely factor 2x3 – 24x2y + 12xy – 144y2 and check your factors for accuracy.

Answer 1

One, rewrite the expression as:
2x^3 + 12xy - 24x^2y - 144y^2

Two, factor the 2x from the first two terms and -24y from the last two terms:
2x(x^2 + 6y) - 24(x^2+6y)

Three, Use the rule for distributive property ab + ac = a(b+c) to finish factoring:
(x^2+6y)(2x-24y)

Answer 2

There....that probably makes more sense...

Answer 3

Whoops, forgot one last thing....

Four, extract 2 from (2x-24y):

2(x-12y)(x^2+6y)

Answer 4

how would you check

Answer 5

Multiply it back out

Answer 6

Factoring is like doing division. The inverse of division is mulitiplication.