Determine all of the following for $f(x) \cdot g(x)$, where $f(x) = -x^2+ 8x - 5$ and $g(x) = x^3 - 11x^2 + 2x$.

Leading term

Leading coefficient

Degree

Constant term

Coefficient of x^2

learnmgcat May 31, 2024

#1**+1 **

First, let's multiply g(x) by f(x). I won't show all the steps cuz I'm a bit lazy....

But make sure use the Distributive property to expand \(\left(\:-x^2+\:8x\:-\:5\right)\left(\:x^3\:-\:11x^2\:+\:2x\right)\).

In the end, we get

\(-x^5+19x^4-95x^3+71x^2-10x\)

The leading term is the term that is first, which is ofcourse, \(-x^5\)

The leading coefficient is the coefficient of the leading term, which is \(-1\)

The degree is the highest raised power, which is \(5\)

The constant term is the term with no x values, which there is none in this case, so \(0\)

The coefficient of x^2 is clearly \(71\)

I hope I answered all of your questions!

Thanks! :)

NotThatSmart May 31, 2024

#1**+1 **

Best Answer

First, let's multiply g(x) by f(x). I won't show all the steps cuz I'm a bit lazy....

But make sure use the Distributive property to expand \(\left(\:-x^2+\:8x\:-\:5\right)\left(\:x^3\:-\:11x^2\:+\:2x\right)\).

In the end, we get

\(-x^5+19x^4-95x^3+71x^2-10x\)

The leading term is the term that is first, which is ofcourse, \(-x^5\)

The leading coefficient is the coefficient of the leading term, which is \(-1\)

The degree is the highest raised power, which is \(5\)

The constant term is the term with no x values, which there is none in this case, so \(0\)

The coefficient of x^2 is clearly \(71\)

I hope I answered all of your questions!

Thanks! :)

NotThatSmart May 31, 2024