I have been informed that on March 7th from 6:00am to 6:00pm Central Time Lamar University will be doing some maintenance to replace a faulty UPS component and to do this they will be completely powering down their data center.
Unfortunately, this means that the site will be down during this time. I apologize for any inconvenience this might cause.
Paul
February 18, 2026
Section 1.4 : Polynomials
3. Perform the indicated operation and identify the degree of the result.
Show All Steps Hide All Steps
Start SolutionHere is the operation we’re being asked to perform.
\[{x^4} + 7{x^3} - 12x - 1 - \left( { - 3{x^2} + 7x + 8} \right)\]Be careful with the order here! We are subtracting the first polynomial from the second and that implies the order we’ve got here. Also be careful with the parenthesis on the second polynomial. We are subtracting the whole polynomial and so we need to have the parenthesis to do that.
Here’s the result of the operation.
\[\begin{align*}{x^4} + 7{x^3} - 12x - 1 - \left( { - 3{x^2} + 7x + 8} \right) & = {x^4} + 7{x^3} - 12x - 1 + 3{x^2} - 7x - 8\\ & = \require{bbox} \bbox[2pt,border:1px solid black]{{{x^4} + 7{x^3} + 3{x^2} - 19x - 9}}\end{align*}\] Show Step 2Remember the degree of a polynomial is just the largest exponent in the polynomial and so the degree of the result of this operation is four.