Andrew factored the expression -30x^3 – 9x^2 – 3x as -5x(6x^2 – 2x-1) . But when Melissa applied the distributive law and multiplied out -5x(6x^2 – 2x – 1), she got -30x^3 + 10x^2 + 5x; thus, Andrew’s solution does not appear to check. Why is that? Please help Andrew to understand this better. Explain your reasoning and correctly factor the original expression, if possible. If the expression is prime, so state.

Question

Andrew factored the expression  -30x^3 – 9x^2 – 3x as -5x(6x^2 – 2x-1) . But when Melissa applied the distributive law and multiplied out -5x(6x^2 – 2x – 1), she got -30x^3 + 10x^2 + 5x; thus, Andrew’s solution does not appear to check. Why is that? Please help Andrew to understand this better. Explain your reasoning and correctly factor the original expression, if possible. If the expression is prime, so state.

anonymous · Answer

He shouldn't have factored by -5x, he effectively divided the 9 by 5 and said it was 2. Which wasn't valid. The real factor is:

anonymous · Answer

Thank you! that one stumped me!

anonymous · Answer

Whoops, hold on. I missed a sign, haha.

anonymous · Answer

ok

anonymous · Answer

attachment

anonymous · Answer

There you go. The 10x^2 +3x +1 doesn't can't be broken down any more. If you apply the quadratic formula, you'll quickly see (as I did).

Best of luck, and watch out for signs. xD

anonymous · Answer

thank you tons! you are amazing!