Question

if p(x) is equal to 2x^3 + 3x ^2+5 x +7 then find the value of p(x) + p(-x)​

Answer 1

$\huge{\underline{\bf\red{QuestiØn} :}}$

$\sf If \: p(x) = 2 {x}^{3} + 3 {x}^{2} + 5x + 7 \: then \\ \sf find \: the \: value \: of \: \boxed{ p(x) + p( - x)}.$

$\huge{\underline{\bf\blue{SolutiØn}\ :}}$

First , Calculate p(x) :-

$\begin{aligned} \\ & \quad \ p(x) = \sf 2 {x}^{3} + 3 {x}^{2} + 5x + 7 \\ \\ & \qquad \qquad \qquad \sf [already \: given] & & & & & & & & \end{aligned}$

Second , Calculate p( -x ) :-

$\begin{aligned} \\ \quad p( - x) & = 2 {( - x)}^{3} + 3 {( - x)}^{2} + 5( - x) + 7 \\ \\ & = 2( - {x}^{3}) + 3( {x}^{2} ) + 5( - x) + 7 \\ \\ & = \sf - 2 {x}^{3} + 3 {x}^{2} - 5x + 7 \\ \end{aligned}$

HENCE ,

$\begin{aligned} \\ & \quad \ \sf p(x) + p( - x) \\ \\ & =( 2 {x}^{3} + 3 {x}^{2} + 5x + 7) + ( - 2 {x}^{3} + 3 {x}^{2} - 5x + 7) \\ \\ & = \cancel{2 {x}^{3} } + 3 {x}^{2} + \cancel{5x} + 7 - \cancel{2 {x}^{3}} + 3 {x}^{2} - \cancel{5x} + 7 \\ \\ & = 3 {x}^{2} + 3 {x}^{2} + 7 + 7 \\ \\ & = \ \boxed{ 6 {x}^{2} + 14} \\ & & & & & \end{aligned}$

$\red{\rule{5.5cm}{0.02cm}}$

$\Large{ \mid {\underline{\underline{\bf\green{BrainLiest \ \ AnswEr}}}} \mid }$

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