Remainder Theorem

Find the remainder when q3+ q2-5q5+q+3 is divided by q-3.

$p\left(z\right)=z+8z^2-4$ and $g\left(z\right)=4+z$, find the remainder when $p\left(z\right)$ is divided by $g\left(z\right)$.

Find the remainder when dividend and divisor are given.

Dividend : y3+1, Divisor : y+1

Find the reminder when c4+4c6+4c+20 divided by c.

Find the value of $\left(14a^{2}b-7a{b}^2\right)÷7ab$.

If $f\left(x\right)=x^4-2x^3+3x^2-ax-b$ when divided by $x-1$, the remainder is $6$, then find the value of $a+b$.

Let $S_1$ and $S_2$ are the remainders when a polynomial $x^3+2x^2-5ax-7$ and $x^3+a{x}^2-12x+6$ are divided by $\left(x+1\right)$ and $\left(x-2\right)$ respectively. If $2S_1-S_2=10$ , find the value of $a$.

If $\left(x^2-7x+a\right)$ has a remainder $1$ when divided by $\left(x+1\right)$, then $a=$

If $\left(x^2-7x+a\right)$ has a remainder $1$ when divided by $\left(x+1\right)$, then $a=$

To obtain the first term of the quotient divide the highest degree term of the dividend by the highest degree term of the _____.

Let $ \text{P}\left(x\right)$ be a polynomial and dividing $ \text{P}\left(x\right)$ by $ (x+1)$ leaves remainder 5.

Which of the following statements is true about remainder theorem?

Suppose, the remainder obtained while dividing $x$ by $61$ is $2$. What is the remainder obtained while dividing $x^7$ by $61$?

If the polynomial $p\left(x\right) =x^4–2x^3+3x^2–ax+3a–7$ when divided by $\left(x+1\right)$ leaves a remainder $19$, then find the value of $a$.