Question

HELP!!!! Been stuck on this problem for 3 days and the explanation given has been no help. I'm Stuck!!
Factor: 6x^3(x-6)-3x(x-6)
the information says look for any factors common to all terms of the expression. The binomial may be the only common factor.

Answer 1

draw big brackets around the left and right sides of your expression.
next, multiply the brackets by the fraction (x-6)/(x-6)
\[[6x ^{3}*(x-6)-3x*(x-6)] * \frac{ x-6 }{ x-6 }\]

then move the denominator of the fraction to beneath the original expression while leaving the numerator outside of the brackets\[[\frac{ 6x ^{3} *(x-6)-3x*(x-6)}{ (x-6) }] *(x-6)\]

Answer 2

distribute the denominator inside of the brackets to each expression.
\[[\frac{ 6x ^{3}*(x-6) }{ (x-6) } + \frac{ -3x*(x-6) }{ (x-6) }] *(x-6)\]

Answer 3

cross out the binomials that appear in the numerator and denominators within the brackets
\[[6*x ^{3}-3x] *(x-6)\]

repeat entire process with the other common factors which are 3 and x.
final answer should be
\[3*x*(x-6)*(2x ^{2}-1)\]

Answer 4

do you see that x-6 is common to both terms?