# Math Help - Factorizing - a true headache

1. ## Factorizing - a true headache

please someone help: penultimate question one of my step paper quizzes;

8x3+6x2-23x+9 or in other words:

Reduce to a binomial expression the sum of eight times a number x raised to the power of three and six times a number x raised to the power of two less the sum of twenty three times a number x and 9.

2. Why not just use the '^' symbol to represent powers?. That's what it's for.

Anyway, there are various ways to tackle these. The Rational Root Theorem is always a choice if it's a toughy.

You can also break it up:

$8x^{3}+6x^{2}-23x+9$

Break it up:

$8x^{3}+18x^{2}-12x^{2}-27x+4x+9$

Group and factor:

$(8x^{3}-12x^{2}+4x)+(18x^{2}-27x+9)$

Factor:

$4x(2x^{2}-3x+1)+9(2x^{2}-3x+1)$

See?. What's in the parentheses is the same.

$(4x+9)(2x^{2}-3x+1)$

Now, the quadratic factors as well. Finish up.