Question

A polynomial $p\left(x\right)$ is divided by $(2x-1)$. The quotient and remainder obtained are $(7x^2+x+5)$ and $4$ respectively. Find $p\left(x\right)$

Answer 1

We know, $p\left(x\right)=\left[g\right(x)\times q(x\left)\right]+r\left(x\right)$ [Division algorithm for polynomials]
$p\left(x\right)=(2x-1)(7x^2+x+5)+4$
$p\left(x\right)=14x^3+2x^2+10x-7x^2-x-5+4$
$p\left(x\right)=14x^3-5x^2+9x-1$
$\therefore$$thedividend$p(x) = 14x^{3} - 5x^{2} + 9x - 1$