SOLUTION: What is the degree and the leading coefficient for x^2 (2x − 3)^2?

Algebra ->  Rational-functions -> SOLUTION: What is the degree and the leading coefficient for x^2 (2x − 3)^2?      Log On


   

Question 1136627: What is the degree and the leading coefficient for x^2 (2x − 3)^2?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
i believe the degree is 4 and the leading coefficient is 4.

if you multiply the factors out, you get:

x^2 * (2x - 3) * (2x - 3) becomes:

(2x^3 - 3x^2) * (2x - 3) which becomes:

4x^4 - 6x^3 - 6x^3 + 9x^2 which simplifies to:

4x^4 - 12x^3 + 9x^2.

since this is already arranged in descending order of degree, then:

the degree is 4 and the leading coefficient is 4.

the original equation is y = x^2 * (2x-3)^2.

the final equation is y = x^4 - 12x^3 + 9x^2.

these two equations are equivalent to each other.

if you graph them both, they will generate the identical curve, as shown below:

$$$