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 and Trigonometry (6th Edition)
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Author:Robert F. Blitzer
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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A function h is defined by:
h(q) = aq+ 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).

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