Question

Explain, in complete sentences, how you would completely factor 2x^3 - 24x^2y + 12xy - 144y^2 and check your factors for accuracy.

Answer 1

try pairing the terms:
no first divide thru by 2:

= 2( x^3 -12x^2y + 6xy - 72y^2 )

now pair terms:
= 2(x^3 + 6xy - 12x^2y - 72y^2)

factor out
= 2[ x(6y +x^2) -12y (6y + x^2)]

two brackets are equal so
= 2(x - 12y)(6y + x^2)

Answer 2

to check we expand in order to hopefully get back to origainal expression
2( 6xy + x^3 -72y^2 - 12x^2_
= 2x^3 -24x^2y + 12xy - 144y^2