could someone please help me understand this?

Question

Factor the following by taking out the greatest common factor.
8x3 +12x2 +16x

i know the common factor is 4. but how do i know for exponents? I'm watching video examples on my homework and there not showing how they come up with the common factor for exponents. i feel like once i figure that part out i will know how to do math problems

Answer 1

8x³ +12x² +16x

 

= 4(2)(x)(x)(x) + 4(3)(x)(x) + 4(4)(x)

 

The greatest common factor in the numbers is 4

The greatest common factor in the variables is x

So the greatest common factor is 4x

 

Dividing each term by 4x we have

 

4x(8x³/4x + 12x²/4x + 16x/4x)

 

= 4x(2x² + 3x + 4)

Answer 2

Each term in the polynomial also has a common factor of x.  So your greatest common factor is actually 4x.  So we factor it as

 

4x(2x² + 3x + 4)

 

 

If you want to know how I got the terms in parentheses, I simply divided the original polynomial by the greatest common factor.