Question

find the remainder when 7x3 - 3x2 + 5x -2 is divided by X+2​

Answer 1

AnswEr:-

Your Answer Is -80.

ExplanaTion:-

Here we can find out the remainder by 2 methods:-

1) Long Division Method:-

$\boxed{\begin{array}\quad\begin{tabular}{m{3.5em}cccc}&& 7x^2& -17x&+39\\\cline{3-6}\multicolumn{2}{l}{x + 2\big)}&7x^3& - 3x^2& + 5x & - 2\\&& 7x^3&+14x^2&&\\&&-&- &&\\ \cline{3-6}&&&-17x^2& + 5x& - 2\\&&&-17x^2&-34x &\\ &&&+&+&\\ \cline{4-6}&&&& 39x& - 2\\&&&&39x&+78\\ &&&&-& -\\ \cline{5-6}&&&&&-80 = remainder. \\ \\\end{tabular}\end{array}}$

$\tt\therefore$ The Remainder Is -80.

2) By Remainder Theorem:-

By remainder theorem we get,

$\tt\mapsto x + 2 = 0. \\ \\ \tt\mapsto x = - 2.$

By putting the value of x in the given polynomial we get:-

$\tt\mapsto7 {x}^{3} - 3 {x}^{2} + 5x - 2. \\ \\ \tt = 7( - 2) {}^{3} - 3( - 2) {}^{2} + 5( - 2) - 2. \\ \\ \tt = 7( - 8) - 3(4) + ( - 10) - 2. \\ \\ \tt = - 56 - 12 - 10 - 2. \\ \\ \tt = - 68 - 12. \\ \\ \tt = - 80 = remainder.$

$\tt\therefore$ The Remainder Is -80.