Mobile Notice
You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best viewed in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (you should be able to scroll/swipe to see them) and some of the menu items will be cut off due to the narrow screen width.
Section 1.4 : Polynomials
10. Perform the indicated operation and identify the degree of the result.
Subtract \(3{\left( {{x^2} + 1} \right)^2}\) from \(6{x^3} - 9{x^2} - 13x - 4\)
Show All Steps Hide All Steps
Start SolutionHere is the operation we’re being asked to perform.
\[6{x^3} - 9{x^2} - 13x - 4 - 3{\left( {{x^2} + 1} \right)^2}\]Now, before we actually do the subtraction we need to actually multiply out the second term before we do the subtraction. Here are the results of all these operations.
\[\begin{align*}6{x^3} - 9{x^2} - 13x - 4 - 3{\left( {{x^2} + 1} \right)^2} & = 6{x^3} - 9{x^2} - 13x - 4 - 3\left( {{x^4} + 2{x^2} + 1} \right)\\ & = 6{x^3} - 9{x^2} - 13x - 4 - 3{x^4} - 6{x^2} - 3\\ & = \require{bbox} \bbox[2pt,border:1px solid black]{{ - 3{x^4} + 6{x^3} - 15{x^2} - 13x - 7}}\end{align*}\] 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.