Question

Find the greatest common factor of the polynomial: 10x^5+15x^4-25x^3

10x^5

x^3

5x^3

5

Answer 1

Third option.

Explanation:

The greatest common factor (GCF) for a polynomial is defined as the largest monomial that divides each term.

Given the polynomial
`10x^5+15x^4-25x^3`, the GCF of the coefficients can be found by descompose each one of them into their prime factors:

`10=2*5\\15=2*5\\25=5*5`

You can observe that the GCF of the coefficients is:

`GFC_((coefficients))=5`

Now you need to find the GCF of the variables. You can notice that each term has at least one x³, then:

`GFC_((variables))=x^3`

Threfore, the GCF of the polynomial is:

`GCF=5x^3`

Answer 2

Option C is correct.

Explanation:

We need to find the greatest common factor of the polynomial

10x^5+15x^4-25x^3

The greatest common factor is the number that is divisible by all 3 terms of the polynomial.

so, the common factor is 5x^3 for above polynomial

Taking out the common factor

5x^3(2x^2+3x-5)

Now the term in the bracket has no other common factor

So, the greatest common factor of 10x^5+15x^4-25x^3 is 5x^3

So, Option C is correct.