Embibe Experts Solutions for Chapter: Polynomials, Exercise 1: Kerala Board-2019

$P\left(x\right)$ is a second degree polynomial with $P\left(1\right)=0$ and $P\left(-2\right)=0$. Find two first degree factors of $P\left(x\right)$.

$P\left(x\right)$ is a second degree polynomial with $P\left(1\right)=0$ and $P\left(-2\right)=0$. Find the polynomial $P\left(x\right)$.

If $x-1$ is a factor of the second degree polynomial $P\left(x\right)=a{x}^2+bx+c$ and $P\left(0\right)=-5$. What is the value of $c$?

If $x-1$ is a factor of the second degree polynomial $P\left(x\right)=a{x}^2+bx+c$ and $P\left(0\right)=-5$. Prove that $a+b=5$.

If $x-1$ is a factor of the second degree polynomial $P\left(x\right)=a{x}^2+bx+c$ and $P\left(0\right)=-5$. Write a second-degree polynomial whose one factor is $x–1$.

If $p\left(x\right)=x^2-7x+13$, what is $p\left(3\right)$?

Write the polynomial $p\left(x\right)-p\left(3\right)$ as the product of two first degree polynomials. When $p\left(x\right)=x^2-7x+13$

Find the solutions of the equation $p\left(x\right)-p\left(3\right)=0$. When $p\left(x\right)=x^2-7x+13$