S Purkayastha Solutions for Chapter: Algebraic Expressions and Identities, Exercise 7: CHECK POINT

Find the quotient and the remainder, when $x^2-81$ is divided by $x+9$.

Find the quotient and the remainder, when $x^3-3x^{2}y+3x{y}^2-y^3$ is divided by $x-y$.

Find the quotient and the remainder, when $2m^4+8m^3+7m^2+4m+3$ is divided by $m^2+4m+3$.

Find the quotient and the remainder, when $y^5+5y^3+3y^2+5y+3$ is divided by $y^2+4y+2$.

Using division, show that $x+5$ is a factor of $x^4+4x^3-2x^2+10x-25$.

Using division, show that $x^2+1$ is not a factor of $x^5-x^4+3x^4+4x^2+4x+6$.

Find the product of $(4p^2-9)$ and $(2p^2-3p+1)$ and divide the product by $2p-3$. Is $2p-3$ a factor of the product?

What must be subtracted from $8x^4+14x^3-2x^2+7x-8$ so that the resulting polynomial is exactly divisible by $4x^2+3x-2$.