Question

I need help understanding if I am doing GFC on polynomials with exponents right.

The problem is 16p^4+4p^3
I got 4 as the GFC and wrote out the equation as 4p^2(4p^2+p)
I get GFC but I am struggling with understanding exponents that don't have a factor.

Answer 1

`GCF\ of\ 16p^4+4p^3 = 4p^3`

The expression can be written as:

`16p^4 + 4p^3 = 4p^3(4p + 1)`

Solution:

Given is:

`16p^4 + 4p^3`

We have to find the greatest common factor

Find GCF of numbers 16 and 4

The factors of 4 are: 1, 2, 4

The factors of 16 are: 1, 2, 4, 8, 16

Then the greatest common factor is 4

Now find GCF of variables

`GCF\ of\ p^4\ and\ p^3`

Here the p is same but exponents are different 4 and 3

Thus GCF is
`p^3`

GCF is the largest number that will divided evenly into that number

Therefore,

`GCF\ of\ p^4\ and\ p^3 = p^3`

Thus GCF of
`16p^4+4p^3` is:

`GCF\ of\ 16p^4+4p^3 = 4p^3`

Thus GCF is found

THE EXPRESSION CAN BE WRITTEN AS:

Factor out the GCF

`16p^4 + 4p^3 = 4p^3(4p + 1)`