The polynomial
R(x)=−7+4x5−3x2+6x5−2x−9x3+x2
is to be studied.
(i) Arrange R(x) in descending powers of x and combine all like terms.
(ii) From the simplified form obtained in part (i), find:
(a) the leading coefficient,
(b) the coefficient of x2, and
(c) the constant term.
(iii) Verify that the sum of all coefficients of the simplified polynomial equals R(1). Calculate R(1) to confirm your answer.