Monica Capoor Solutions for Chapter: Factorisation, Exercise 8: EXERCISE

Divide $x^3-14x^2+37x-26$ by $x^2-12x+13$.

Dividing $a^4+a^2+1$ by $a^2+a+1$ gives $a^2-a+k$. Find the value of $k$.

Dividing $10a^4+17a^3-62a^2+30a-3$ by $2a^2+7a-1$ gives $5a^2-9a+k$. Find the value of $k$.

Dividing $6x^5+15x^4+16x^3+4x^2+10x-35$ by $2x^3+5x^2+2x-7$, if the quotient is of the form $a{x}^2+b$, then find the value of $\left(a+b\right)$.

Dividing $\left(y^5+y^4+y^3+y^2+y+1\right)$ by $\left(y^3+1\right)$ gives $y^2+y+k$. Find the value of $k$. 

The product of two expressions is $y^2-z^2+2xy-2xz.$ If one of them is $2x+y+z$, find the other.

Find the value of $a$ so that $1-7x$ is a factor of $-14x^3-47x^2-14x+a$.

What must be added to $a^4+2a^3-2a^2+a-1$, so that the resulting polynomial is exactly divisible by $a^2+2a-3$?