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)}`