Question

Question 2
Find p(0), p(1) and p(2) for each of the following polynomials:
(i) $p\left(y\right)=y^2-y+1$
(ii) $p\left(t\right)=2+t+2t^2-t^3$
(iii) $p\left(x\right)=x^3$
(iv) $p\left(x\right)=(x-1)(x+1)$

Answer 1

(i) $p\left(y\right)=y^2-y+1p\left(0\right)=0^2-0+1=1p\left(1\right)=1^2-1+1=1$
$p\left(2\right)=2^2-2+1=3.$

(ii) $p\left(t\right)=2+t+2t^2-t^{3}p\left(0\right)=2+0+2\times 0^2-0^3=2p\left(1\right)=2+1+2\times 1^2-1^3=4$
$p\left(2\right)=2+2+2\times 2^2-2^3=4+8-8=4.$

(iii) $p\left(x\right)=x^{3}p\left(0\right)=0p\left(1\right)=1$
$p\left(2\right)=8.$

(iv) $p\left(x\right)=(x-1)(x+1)p\left(0\right)=(-1)\left(1\right)=-1p\left(1\right)=(1-1)(1+1)=0$
$p\left(2\right)=(2-1)(2+1)=3$