I need help with this math problem?

Question

Factor the following by taking out the greatest common factor.

8x³ +3x²

 

but neither have a factor. please help me

Answer 1

Michael, get a grip!!

See --  https://www.wyzant.com/resources/answers/190191/could_someone_help_me_find_the_gcf

 

You are wrong to say that neither 8x³ nor 3x² have factors.

The factors of 8x³ are:   1, 2, 4, 8, x, x², x³      [they all divide into 8x3 evenly] 

 The factors of 3x² are:   1, 3, x x²   [they all divide into 3x2 evenly]

 

Now, which factor is the largest (greatest) one that they share (common)?

  [note: given that x could represent any number, we leave it that way]

 

So, looks like there is no number, but there is an x² that is the largest shared factor.  Let's factor out the x²:

    x²(8x+3)

 

Here, try this one:

    What is the GCF of:     21x2 + 7x

Answer 2

8x³ + 3x²

 

Both are divisible by x²

8x³+3x² = 8(x²)(x)+3x²

factor x² from both terms

 

x²(8x + 3) is the answer

 

********************

Think of this in the fact that x 

represents a number.  What if

x was 2?  We would have

 

8(2³) + 3(2²)

= 8(8) + 3(4)

= 8(4)(2) + 3(4)

You can see that both are divisible by 4

= 4[8(2) + 3]

= 2²[8(2) + 3]

Putting x back in place of 2 we have

x²(8x+3)