GrareeCowui

2022-01-30

What is the leading term, leading coefficient, and degree of this polynomial $f\left(x\right)=-2{x}^{3}{\left(x+5\right)}^{4}{\left(x-3\right)}^{2}$?

Jordyn Horne

Expert

Explanation:
You first express the the polynomial in its canonical form consisting of a conbination of monomials, you get:
$-2{x}^{9}-8{x}^{8}-198{x}^{7}+620{x}^{6}+2050{x}^{5}-1500{x}^{4}-11250{x}^{3}$
The degree is the term with the greatest exponent, which is in this case 9.
The leading term is $-2{x}^{9}$, and the leading coefficient is -2, and the degree of this polynomial is 9.

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