The polynomial function p(x)= (2x^ 2 -3x+1)(-4x^ 3 +5)-7x^ 4 +9 is to be analysed.
MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions
Problem
The polynomial function
p(x)=(2x2−3x+1)(−4x3+5)−7x4+9
is to be analysed.
(i) Without fully expanding the expression, determine the degree and the leading coefficient of p(x), giving clear reasons for each.
(ii) Expand only the terms necessary to verify the leading coefficient found in part (i).
(iii) Using the degree and the leading coefficient, describe the end behaviour of the graph of y=p(x) as x→±∞. State your conclusions in one or two sentences.