Question

Factor completely 30x^4+45x

Answer 1

In this problem, we want to complete factor a given expression:

$30x^4+45x$

We will begin by finding the greatest common factor for the two terms. Let's begin with 30 and 45.

The Greatest Common Factor of 30 and 45 is:

$GCF(30,45)=15$

Then, we find the greatest common factor of x⁴ and x:

$GCF(x^4,x)=x$

So the greatest common factor of both terms is:

$GCF(30x^4,45x)=15x$

When we factor this, it means we are dividing the greatest common factor from the two terms to pull it out of the expression.

$30x^4+45x=15x(2x^3)+15x(3)$

We can pull the 15x outside a group of parentheses to get:

$\boxed{15x(2x^3+3)}$