Find the remainder when x^{3}+3x^{2}+3x+1 is | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

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

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(A) Let $p(x) = x^{3}+3x^{2}+3x+1$.According to the Remainder Theorem,when a polynomial $p(x)$ is divided by $(x - a)$,the remainder is $p(a)$.Here,the divisor is $x + 1$,which can be written as $x - (-1)$. Thus,$a = -1$.To find the remainder,we calculate $p(-1)$:$p(-1) = (-1)^{3} + 3(-1)^{2} + 3(-1) + 1$$p(-1) = -1 + 3(1) - 3 + 1$$p(-1) = -1 + 3 - 3 + 1$$p(-1) = 0$.Therefore,the required remainder is $0$.

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

Similar Questions

Verify: $x^{3}-y^{3}=(x-y)(x^{2}+xy+y^{2})$

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

Check whether $7+3x$ is a factor of $3x^3+7x$.

Find the value of $k$,if $x - 1$ is a factor of $p(x)$ in this case: $p(x) = x^{2} + x + k$.

Verify whether the following are zeroes of the polynomial indicated against them:
$p(x) = 3x^2 - 1, x = -\frac{1}{\sqrt{3}}, \frac{2}{\sqrt{3}}$

Vedclass Test Series

Exam Paper Generator

Online Exam Module