Algebra 1 Help!?

Question

FACTORING POLYNOMIALS

I have two problems.

1) Factor.

x^6 - 2x^5 + 7x^4

My answer is "not factorable." (Which means that it's impossible to factor.) My friend graded this, and she marked it wrong... Is my answer correct?

2) Factor.

m^4 + 8m^3 + 8m^2 +64m

My answer is (m + 8)(m^3 + 8m). Like I typed, my friend marked my answer wrong... Is my answer correct?

If I am wrong, please explain these two problems to me (and show your work).

If I am right, please tell me so.

Thanks for helping me!

Answer 1

PROBLEM 1:

You can pull out a common x^4:

x^4( x² - 2x + 7)

The part inside the parenthese cannot be factored with integers, but your friend is right that you could have factored further.

PROBLEM 2:

Again you can pull out a common m to begin with:

m(m^3 + 8m² + 8m + 64)

Then you can factor this as:

m(m + 8)(m² + 8)

I think you have the concepts, but you just forgot to look for cases where just the variable is repeated at different powers. Other than that you had it right.

Answer 2

Just factor out the GCF in both cases.

1} x^6 - 2x^5 + 7x^4= x^4(x^2 - 2x + 7)

2} m(m^3 + 8m^2 + 8m +64)

Answer 3

Simplifying
x^6 + -2x^5 + 7x^4

Reorder the terms:
7x^4 + -2x^5 + x^6

Factor out the Greatest Common Factor (GCF), 'x^4'.
x^4(7 + -2x + x^2)

Final result:
x^4(7 + -2x + x^2)



Simplifying
m^4 + 8m^3 + 8m^2 + 64m

Reorder the terms:
64m + 8m^2 + 8m^3 + m^4

Factor out the Greatest Common Factor (GCF), 'm'.
m(64 + 8m + 8m^2 + m^3)

Final result:
m(64 + 8m + 8m^2 + m^3)

Answer 4

x^6-2x^5+7x^4=

x^4(x^2-2x+7)

m^4+8m^3+8m^2+64m

m(m^3+8m^2+8m+64)
m(m+8)(m^2+8)

Answer 5

I have never seen this kind of factorizing problem!

Answer 6

oh whoa i don't know... did you try using the quadratic formula?