Disha Expert Team Solutions for Chapter: Polynomials and Rational Expressions (Factorization, Factor & Remainder Theorem), Exercise 1: Exercise

If $\left(x+2\right)$ and $\left(x-1\right)$ are the factors of $\left(x^3+10x^2+mx+n\right)$, the value of $m$ and $n$ are _____.

For what value of $k$, is the polynomial $2x^4+3x^3+2k{x}^2+3x+6$ exactly divisible by $\left(x+2\right)$?

If $4x^4-3x^3-3x^2+x-7$ is divided by $1-2x$, then remainder will be-

If the polynomial $\left(2x^3+a{x}^2+3x-5\right)$ and $\left(x^3+x^2-2x+a\right)$ leave the same remainder when divided by $\left(x-2\right)$, find the value of $a$?

lf $(x-1)$ and $\left(x-2\right)$ are two factors of $x^3 - a{x}^2 + 14x + b$, the values of $a$ and $b$ are:

Let $r1$ and $r2$ be the remainders when the polynomials $p\left(x\right)=x^3+x^2-5kx-7$ and $q\left(x\right) = x^3+ k{x}^2-12x +6$ are divided by $x+1$ and $x-2$ respectively. If $2r_1 - r_2 = 10$, the value of $k$ is _____.

If $x=\frac{4}{3}$ is a root of the polynomial $f\left(x\right)=6x^3-11x^2+kx-20,$ then find the value of $k$?

If two zeroes of the polynomial $x^4-6x^3-26x^2+138x-35$ are $2\pm \sqrt{3}$, then the other zeroes are _____.