Asked by Anonymous
                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
            
        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
Answers
                    Answered by
            Anonymous
            
    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
    
4x^4 - 8x^3 + 4x^2
with my degree being 4 and leading coefficient being 4
Someone tell me if I'm wrong
                    Answered by
            oobleck
            
    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.
    
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.
                    Answered by
            Anonymous
            
    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!
    
Thank you for showing me other ways!
                    Answered by
            oobleck
            
    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.
    
When you factor out the 2, you get 4x^2(x-1)^2 so the leading coefficient is clearly 4.
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