1. ## polynomial

the polynomial p(x) = $x^4+ax^3-10x^2+bx-12$ is divisible by d(x) = $(x+4)(x-3)$ Calculate the quotient of the division of P(x) of D(x).

$x^2+x+1$

2. Originally Posted by Apprentice123
the polynomial p(x) = $x^4+ax^3-10x^2+bx-12$ is divisible by d(x) = $(x+4)(x-3)$ Calculate the quotient of the division of P(x) of D(x).

$x^2+x+1$
Dividing $x^4+ax^3-10x^2+bx-12$ by d(x) = $(x+4)(x-3)$ gives
$x^2+(a-1)x+3-a$ and a rest $(b+13a-15)x+12 (2-a)$
Quotient is $x^2+x+1$