Question

find m(-1) -m(2) for the polynomial m(x) = 4x^3 +3x^2-4x-3.​

Answer 1

$\large\sf\underline{Given\::}$

Polynomial :

• $\bf\:m(x) =4x^{3}+3x^{2}-4x-3$

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$\large\sf\underline{To\:find\::}$

• Value of $\bf\:m(-1) -m(2)$

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$\large\sf\underline{Concept\:to\:be\:used\::}$

In this question we are given a polynomial , we need to find m ( - 1 ) - m ( 2 ) . Looks somewhat complicated right !? . But it's very simple. We will solve this problem in 3 steps.

In the first step we will find the value of m ( - 1 ) by substituiting ( - 1 ) in place of x in the given polynomial.

In the second stepwe will find the value of m ( 2 ) by substituiting ( 2 ) in place of x in the given polynomial.

Then at last we would find their difference.

Hope I sound clear , let's begin !

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$\large\sf\underline{Solution\::}$

$\large\sf\underline{1^{st}\:Step\::}$

Let's find the value of m ( - 1 ) by substituiting x as ( - 1 ) in the given polynomial :

Given polynomial = $\bf\:m(x) =4x^{3}+3x^{2}-4x-3$

$\sf\implies\:m(-1) =4(-1)^{3}+3(-1)^{2}-4(-1)-3$

• Taking the numbers out of their square and cube

$\sf\implies\:m(-1) =4 \times (-1)+3 \times 1 -4 \times (-1)-3$

• Multiplying the terms

$\sf\implies\:m(-1) =-4+3+4-3$

• Numbers with opposite signs gets cancelled out

$\sf\implies\:m(-1) =-\cancel{4}+\cancel{3}+\cancel{4}-\cancel{3}$

$\small{\underline{\boxed{\mathrm\red{\implies\:m\:(-1)\:=\:0}}}}$ ✧

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$\large\sf\underline{2^{nd}\:Step\::}$

Let's find the value of m ( 2 ) by substituiting x as ( 2 ) in the given polynomial :

Given polynomial = $\bf\:m(x) =4x^{3}+3x^{2}-4x-3$

$\sf\implies\:m(2) =4(2)^{3}+3(2)^{2}-4(3)-3$

• Taking the numbers out of their square and cube

$\sf\implies\:m(-1) =4 \times 8 +3 \times 4 -4 \times 2-3$

• Multiplying the terms

$\sf\implies\:m(-1) =32+12-8-3$

• Doing simple calculations

$\sf\implies\:m(-1) =44-8-3$

$\sf\implies\:m(-1) =36-3$

$\small{\underline{\boxed{\mathrm\red{\implies\:m\:(2)\:=\:33}}}}$ ✧

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$\large\sf\underline{3^{rd}\:Step\::}$

Let's find difference of m ( - 1 ) and m ( 2 ) :

$\sf\:m(-1) -m(2)$

Substituiting the value of :

• m ( - 1 ) as = $\tt\blue{0}$

• m ( 2 ) as = $\tt\blue{33}$

We get :

$\sf\leadsto\:0 -33$

$\small{\underline{\boxed{\mathrm\red{\leadsto\:-33}}}}$ ⍟

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!! Hope it helps !!