Maharashtra Board Solutions for Chapter: Polynomials, Exercise 7: Problem set

On adding the following polynomials $7x^4-2x^3+x+10; 3x^4+15x^3+9x^2-8x+2$ we get $a{x}^4+b{x}^3+9x^2-7x+12$, find the value of $a+b$

On adding the following polynomials $3p^{3}q+2p^{2}q+7; 2p^{2}q+4pq-2p^{3}q$ we get $p^{3}q+a{p}^{2}q+bpq+7$, find the value of $a-b$.

Divide polynomial $3x^3-8x^2+x+7$ by $x-3$ using synthetic method and write the quotient and remainder.

At the end of the year $2016$, the population of villages Kovad, Varud, Chikhali is $5x^2-3y^2, 7y^2+2xy \mathrm{and} 9x^2+4xy$ respectively. At the beginning of the year $2017, x^2+xy-y^2, 5xy \mathrm{and} 3x^2+xy$ persons from each of the three villages respectively went to another village for education. If the remaining total population of these three villages is $a{x}^2+b{y}^2-xy$, find the value of $a+b$.

Polynomials $b{x}^2+x+5$ and $b{x}^3-2x+5$ are divided by polynomial $x-3$ and the remainders are $m$ and $n$ respectively. If $m-n=0$ then find the value of $b$.

If the simplification of $\left(8m^2+3m-6\right)-\left(9m-7\right)+\left(3m^2-2m+4\right)$ is $a{m}^2+bm+c$, find $a+b+c$.

If polynomial $a{x}^2+bx+c$ is to be subtracted from $x^2+13x+7$ to get the polynomial $3x^2+5x-4$, find $a+b+c$.

Which polynomial is to be added to $4m+2n+3$ to get the polynomial $6m+3n+10$?