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avatar+1981 

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

 Jul 1, 2024
 #1
avatar+1271 
+1

Let's first multiply the two functions to make our lives really easy. We have

\(( -x^2+ 8x - 5)(x^3 - 11x^2 + 2x)\\ -\left(x^{5}-11x^{4}+2x^{3}\right)+8x\left(x^{3}-11x^{2}+2x\right)-5\left(x^{3}-11x^{2}+2x\right)\\-x^{5}+19x^{4}-95x^{3}+71x^{2}-10x\)

 

The leading term is \(-x^5\)

The leading coefficient is \(-1\)

The degree of the polynomial is the highest power appearing in the polynomial, which in this case, is 5. 

The constant term is the one with no x value. Since there is no constant, the constant is just 0. 

The coefficient of x^2 is \(71\)

 

Thanks! :)

 Jul 1, 2024

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