Question

I have to find the degree and leading coefficient for polynomial:
x^2(2x- 2)^2

My question is do I have to multiply (2x-2) x (2x-2) then multiply that by x^2?
Someone please help me out

Answer 1

I ended up with
4x^4 - 8x^3 + 4x^2

with my degree being 4 and leading coefficient being 4
Someone tell me if I'm wrong

Answer 2

of course you have to
multiply (2x-2) x (2x-2) then multiply that by x^2
!!!

why would you think otherwise?
Of course, you could multiply x^2 (2x-2) and then again by (2x-2), since multiplication is associative and commutative.
Or, you could factor out the 2, and make that 4x^2(x-1)^2. or 2(x-1)*x^2*(2x-2)

But yes, your answer is correct.

Answer 3

I just wasn't sure if we had to leave it as is or multiply it all the way through.
Thank you for showing me other ways!

Answer 4

actually, you didn't really have to expand it out. You know from the expression that it is degree 4.
When you factor out the 2, you get 4x^2(x-1)^2 so the leading coefficient is clearly 4.