(A) Let $p(x) = x^4+x^3-2x^2+x+1$.According to the Remainder Theorem,if a polynomial $p(x)$ is divided by $(x-a)$,the remainder is $p(a)$.Here,the div

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(A) Let $p(x) = x^4+x^3-2x^2+x+1$.According to the Remainder Theorem,if a polynomial $p(x)$ is divided by $(x-a)$,the remainder is $p(a)$.Here,the divisor is $x-1$,so $a = 1$.Now,calculate $p(1)$:$p(1) = (1)^4 + (1)^3 - 2(1)^2 + 1 + 1$$p(1) = 1 + 1 - 2(1) + 1 + 1$$p(1) = 1 + 1 - 2 + 1 + 1$$p(1) = 2$.Therefore,the remainder is $2$.

Class 9 Mathematics Polynomials Textbook - Polynomials

Medium

Find the remainder when $x^4+x^3-2x^2+x+1$ is divided by $x-1$.

A
$2$
B
$3$
C
$4$
D
$5$

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Verify whether the following is a zero of the polynomial indicated against it:
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Easy

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Verify whether the following is a zero of the polynomial indicated against it:
$p(x) = 5x - \pi, \, x = \frac{4}{5}$

Easy

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Classify the following as linear,quadratic,and cubic polynomials:
$(i)$ $1+x$
$(ii)$ $3t$
$(iii)$ $r^{2}$
$(iv)$ $7x^{3}$

Medium

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Find the remainder when $x^{3}+3x^{2}+3x+1$ is divided by $x$.

Medium

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Find the value of the following polynomial at the indicated value of the variable: $p(t) = 4t^4 + 5t^3 - t^2 + 6$ at $t = a$.

Easy

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Find the remainder when $x^4+x^3-2x^2+x+1$ is divided by $x-1$.

Similar Questions

Verify whether the following is a zero of the polynomial indicated against it:$p(x) = 2x + 1, \, x = \frac{1}{2}$

Verify whether the following is a zero of the polynomial indicated against it:$p(x) = 5x - \pi, \, x = \frac{4}{5}$

Classify the following as linear,quadratic,and cubic polynomials:$(i)$ $1+x$$(ii)$ $3t$$(iii)$ $r^{2}$$(iv)$ $7x^{3}$

Find the remainder when $x^{3}+3x^{2}+3x+1$ is divided by $x$.

Find the value of the following polynomial at the indicated value of the variable: $p(t) = 4t^4 + 5t^3 - t^2 + 6$ at $t = a$.

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Verify whether the following is a zero of the polynomial indicated against it:
$p(x) = 2x + 1, \, x = \frac{1}{2}$

Verify whether the following is a zero of the polynomial indicated against it:
$p(x) = 5x - \pi, \, x = \frac{4}{5}$

Classify the following as linear,quadratic,and cubic polynomials:
$(i)$ $1+x$
$(ii)$ $3t$
$(iii)$ $r^{2}$
$(iv)$ $7x^{3}$