# Factoring Fully.

I am completely confused as to what to do, I don't understand how to factor with the brackets.

$$42x^7(a+10)+60x^5(a+10)-24x^2(a+10)$$

Also state factoring used... Please and thank you. Steps?!?!

• What do you know about $a$? Is it an arbitrary value? Also you can trivially factor out an $x^2$ – ruler501 Mar 26 '14 at 19:13
• Try factoring out the greatest common factor. – John Habert Mar 26 '14 at 19:13
• @Amzoti can't that be factored further? – ruler501 Mar 26 '14 at 19:17

We can treat $(a+10)$ as just another variable, like $x$. We see that $(a+10)$ occurs in every term, and so we can factor it out.
Also, there is a factor $x^2$ in every term.
Also, every term can be divided evenly by $6$.
The largest factor common to each term is thus $6 \cdot x^2 \cdot (a+10)$. In this way we can write the factorized expression as:
$$6x^2(a+10) \cdot \left( 7x^5 + 10x^3 - 4 \right)$$
$(a+10)$ is just a term. Distribute it out and you are left with $(a+10)$ times a polynomial in $x$. Now there is a power of $x$ common to all three terms, so distribute that power of $x$ out. Now look at the coefficients-do they have a common factor?