Question

the remainder when the polynomial f(x)=x^3+x^2 is divided by x+1 is equal to​

Answer 1

(x^3+x^2) / (x +1) = x^2

quotient = x^2

remainder =0

Answer 2

Answer:

$\large{ \sf{ \underline{ \underline{❥Question}}}}$

The remainder when the polynomial $\sf \: f(x)=x ^{3} +x^2$ is divided by $\sf \: x + 1$ is equal to

$\large{ \sf{ \underline{ \underline{❥Answer}}}}$

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

The value of remainder when the polynomial $\sf \: f(x)=x ^{3} +x^2$ is divided by $\sf \: x + 1$.

$\large{ \sf{ \underline{Theorem \: used :}}}$

Remainder Theorem :

Let p(x) be any polynomial of degree greater than or equal to one and let a any real number. If p(x) is divided by the linear polynomial x - a, then the remainder is p(a).

$\large{ \sf{ \underline{Solⁿ :}}}$

Zero of x + 1

$\large \sf⟹x + 1 = 0$

$\large \sf⟹x = - 1$

Now, using Remainder theorem

$\sf \: p(x) = x {}^{3} + {x}^{2}$

$\sf∴p( - 1) = ( - 1) {}^{3} + {( - 1)}^{2}$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = - 1 + 1$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =0$

Hence, 0 is the remainder when the polynomial $\sf \: f(x)=x ^{3} +x^2$ is divided by $\sf \: x + 1$.

$\sf \large{Hope \: it \: helps...}$

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