Question

Factor the expression completely.

$30x^3+15x^4$

Short answer

The solution$30x^3+15x^4=15x^3\left(2+x\right)$

Step-by-step solution

Step 1. Apply the concept of distributive property.

If A, B and C are real numbers, then

$A\left(B+C\right)=\left(B+C\right)A=AB+AC$

Step 2. Analyze the expression.

Given$30x^3+15x^4$

Let us consider first two terms,$30x^3,15x^4$

30, 15 have greatest common factor 15

$x^3,x^4$have greatest common factor$x^3$

So, the greatest common factor of the two terms is$15x^3$

Step 3. Factor the polynomial.

Now, using the distributive property the polynomial can be factored as:

$30x^3+15x^4=15x^3\left(2+x\right)$