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# Algebra

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

Degree

Constant term

Coefficient of x^2

May 31, 2024

#1
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+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 $$71$$

Thanks! :)

May 31, 2024

#1
+806
+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 $$71$$