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
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
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.
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!
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.
To find the degree and leading coefficient for the polynomial x^2(2x-2)^2, you can follow these steps:
1. Multiply (2x-2) by (2x-2) using the FOIL method, which stands for First, Outer, Inner, and Last:
(2x-2)(2x-2) = 2x * 2x + 2x * (-2) + (-2) * 2x + (-2) * (-2)
= 4x^2 - 4x - 4x + 4
= 4x^2 - 8x + 4
2. Now, multiply the result from step 1 by x^2:
x^2 * (4x^2 - 8x + 4) = x^2 * 4x^2 + x^2 * (-8x) + x^2 * 4
= 4x^4 - 8x^3 + 4x^2
The polynomial x^2(2x-2)^2 simplifies to 4x^4 - 8x^3 + 4x^2.
- The degree of a polynomial is the highest power of the variable. In this case, the highest power is 4, so the degree of the polynomial is 4.
- The leading coefficient is the coefficient of the term with the highest power. In this case, the term with the highest power is 4x^4, so the leading coefficient is 4.
Therefore, the degree of the polynomial is 4, and the leading coefficient is 4.