A function h is defined by: h(q) = aq3 + q2 + bq-240 When h(q) is divided by (4-q), the remainder is 72. Also, (2q - 5) is a factor of h(q). i. Calculate the values of a and b. ii. Hence or otherwise, determine all the factors of h(q).

A function h is defined by: h(q) = aq3 + q2 + bq-240 When h(q) is divided by (4-q), the remainder is 72. Also, (2q - 5) is a factor of h(q). i. Calculate the values of a and b. ii. Hence or otherwise, determine all the factors of h(q).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.1: Polynomial Functions Of Degree Greater Than

Problem 49E

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Question

A function h is defined by:
h(q) = aq³+ q²+ bq-240
When h(q) is divided by (4-q), the remainder is 72. Also, (2q - 5) is a factor of
h(q).
i. Calculate the values of a and b.
ii. Hence or otherwise, determine all the factors of h(q).

Expert Solution