Question

by If p(x) = 2x - 11x2 - 4x +5 and g(x) = 2x +1, show that g(x) is not a
factor of p(x).​

Answer 1

Given:

$\Rightarrow{p(x)\: =\: 2x - 11x2 - 4x +5 \:and\: g(x)\: = \:2x +1}$

To find:

$\Rightarrow{show \:that\: g(x)\: is \:not \:a\:factor /:of \:p(x).}$

Solution :

$\Rightarrow{ g(n)\:=\:0}$

2n+1=0

n=-1/2

$\Rightarrow{p(n)\:=\:2n^3-11n^2-4n+5$

$\Rightarrow{p(-1/2)\:=\:2×(-1/2)^3-11×(-1/2)^2-4×-1/2$

$\Rightarrow{p(-1/2)\:=\:2×-1/8-11×1/4+2+5$

$\Rightarrow\rm{-1/4-11/4+7}$

$\Rightarrow\rm{-12/4+7}$

$\Rightarrow\rm{-3+7\:=\:4}$

$\large{\sf{\pink{Reminder\:=\:p(-1/2)\:=\:4 \:is \:not \:equal \:to \:0}}}$

$\huge{\sf{\blue{hence\: g(n)\:is\:not\: factor\:of\:p(n)}}}$

Proved

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