Let , and . (i) Form the polynomial and simplify completely. (ii) Determine the…

MATHEMATICS · Subjective · GCSE · Mathematics · Algebra · Algebra

Problem

Let

f(x)=x^{2}-3x+2

g(x)=2x^{3}+x-1

and

h(x)=5-x

. (i) Form the polynomial

P(x)=(f(x)+g(x))\,h(x)

and simplify completely. (ii) Determine the degree and the leading coefficient of

P(x)

. (iii) Find the value of

P(1)

. (iv) Confirm that the domain of

P(x)

\mathbb{R}