Question

Divide polynomial 4x^4 – 3x^2 + 2x – 7 by polynomial 2x – 1 and find the remainder.

Answer 1

$\: Divide \: polynomial \: \color{red}{ 4x^4 – 3x^2 + 2x – 7 } \: by \\\: polynomial \color{red} \:{ 2x – 1 } \color{black}\: and \: find \: \\\ the \: remainder. \\ \\ \color{khaki}solution \\ \color{greenyellow}given\\\color{blue} 2x - 1 = 0 \\ \color{blue}2x = 1 \\ \color{blue}x = \frac{1}{2} \\ \\ \color{violet}remainder \: theorem \\ \\ \color{blue}p(x) = 4 {x}^{4} - 3 {x}^{2} + 2x - 7 \\ \\ \color{blue}p( \frac{1}{2} ) = 4( { \frac{1}{2} )}^{4} - 3( { \frac{1}{2}) }^{2} + 2( \frac{1}{2} ) - 7 \\ \\ \color{blue} = 4( \frac{1}{16} ) - 3( \frac{1}{4} ) + \frac{2}{2} - 7 \\ \\ \color{blue} = \frac{4}{16} - \frac{3}{4} + \frac{2}{2} - 7 \\ \\ \color{blue} = \frac{4 - 12 + 16 - 112}{16} \\ \\\color{blue} = \frac{20 - 124}{16} \\ \\ \color{blue} = \frac{ - 104 \div 8}{16 \div 8} \\ \\ \color{blue} = \frac{13}{2} \: \color{darkgreen}\: is \: the \: remainder \\ \\ \color{blue}hope \: its \: help \: you☺ \\ \\\color{darkred} its \: ᭄亗 乄 ＭꫝղᎥនh 乄 亗✯❤࿐$