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 views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (should be able to scroll to see them) and some of the menu items will be cut off due to the narrow screen width.
Section 1.4 : Polynomials
1. Perform the indicated operation and identify the degree of the result.
Add \(4{x^3} - 2{x^2} + 1\) to \(7{x^2} + 12x\)
Show All Steps Hide All Steps
Start SolutionHere is the operation we’re being asked to perform.
\[\left( {4{x^3} - 2{x^2} + 1} \right) + \left( {7{x^2} + 12x} \right)\]Note that the parenthesis are only there to illustrate how each polynomial is being used in the indicated operation and are not needed (or used) in general.
Here’s the result of the operation.
\[\left( {4{x^3} - 2{x^2} + 1} \right) + \left( {7{x^2} + 12x} \right) = \require{bbox} \bbox[2pt,border:1px solid black]{{4{x^3} + 5{x^2} + 12x + 1}}\] 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 three.