Solve The remainder when x ^ 31 + 31 is divided by x + 1 is | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$x ^ { 31 } + 31 x + 1$$

Differentiate w.r.t. x

$31\left(x^{30}+1\right)$

Steps Using Derivative Rule for Sum

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is $0$. The derivative of $ax^{n}$ is $nax^{n-1}$.

$$31x^{31-1}+31x^{1-1}$$

Subtract $1$ from $31$.

$$31x^{30}+31x^{1-1}$$

Subtract $1$ from $1$.

$$31x^{30}+31x^{0}$$

For any term $t$ except $0$, $t^{0}=1$.

$$31x^{30}+31\times 1$$

For any term $t$, $t\times 1=t$ and $1t=t$.

$$31x^{30}+31$$

Evaluate

$x^{31}+31x+1$