Question

Find the leading coefficient of the polynomialx^2(3x-4)^2

Answer 1

`x^2(3x-4)^2`
`\begin{gathered} (a-b)^2=a^2-2ab+b^2 \\ \\ (3x-4)^2=(3x)^2-2(3x)(4)+4^2 \\ (3x-4)^2=9x^2-24x+16 \\ \\ a(b+c+d)=ab+ac+ad \\ \\ x^2(9x^2-24x+16)=9x^2(x^2)-24x(x^2)+16(x^2) \\ x^2(9x^2-24x+16)=9x^4-24x^3+16x^2 \end{gathered}`

As you can see above the given polynomial simplified is equal to:

`x^2(3x-4)^2=9x^4-24x^3+16x^2`

The leading coefficient is the coefficient of the term of highest degree.

The term with highest degree in the given polynomial is:

`9x^4`

Then, the leading coefficient is 9