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 5.1 : Dividing Polynomials
6. Use synthetic division to divide \(5{x^4} + {x^2} - 8x + 2\) by \(x - 4\).
Show All Steps Hide All Steps
Start SolutionHere is the synthetic division. We’ll leave it to you to check all the numbers.
\[\begin{array}{*{20}{r}}{\left. {\underline {\,4 \,}}\! \right| }\\{}\\{}\end{array}\,\,\,\,\begin{array}{*{20}{r}}5&0&1&{ - 8}&2\\{}&{20}&{80}&{324}&{1264}\\\hline5&{20}&{81}&{316}&{1266}\end{array}\] Show Step 2The answer is then,
\[5{x^4} + {x^2} - 8x + 2 = \left( {x - 4} \right)\left( {5{x^3} + 20{x^2} + 81x + 316} \right) + 1266\]Note that we only gave one form of the answer (unlike the first couple of problems) since this is often the form we need when using synthetic division and it is also the form that method is set up to give.