Question

$p\left(x\right)=x^2-3x+2,q\left(x\right)=3x+1$
(a) Find $p\left(x\right)+q\left(x\right)$
(b) If $p\left(x\right)+q\left(x\right)+r\left(x\right)=0$, find $r\left(x\right)$.
(c) What number is $p\left(1\right)+q\left(1\right)+r\left(1\right)$?

Answer 1

(a) $P\left(x\right)+q\left(x\right)=x^2-3x+2+3x-1=x^2+1$

(b) $P\left(x\right)+q\left(x\right)+r\left(x\right)=0\Rightarrow x^2+1+r\left(x\right)=0$

$\Rightarrow r\left(x\right)=-x^2-1$

(c) $P\left(1\right)+q\left(1\right)+t\left(1\right)=0.\left(bczP\right(x)+q(x)+r(x)=0)$