Factoring Fully.

Question

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?!?!

Answer 1

$(a+10)$ 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?

Answer 2

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:

$$6x^2(a+10) \cdot \left( 7x^5 + 10x^3 - 4 \right)$$