F2016 The polynomial f(x)= ar +7x²-9x+b is divisible by 2x-1. The remainder when f(x) is divided by x-2 is 5 times the remainder when f(x) is divided by x + 1. (i) Show that a = 6 and find the value of b. ) Using the values from part (i), show that f(x) = (2x - 1)(cx² + dx + e), where c, d and e are integers to be found. Hence factorise f(x) completely. CamScanner로 스캔하기 KS VENT

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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PAPER 1
5. FACTORS OF POLYNOMIALS
page 27
F2016
1
The polynomial f(x)= ar +7x²-9x+b is divisible by 2r-1. The remainder when f(x) is
divided by x-2 is 5 times the remainder when f(x) is divided by x + 1.
(i) Show that a = 6 and find the value of b.
(ii) Using the values from part (i), show that f(x) = (2x − 1)(cx² + dx + e), where c, d and e are
integers to be found.
(iii) Hence factorise f(x) completely.
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KS VENT
Transcribed Image Text:PAPER 1 5. FACTORS OF POLYNOMIALS page 27 F2016 1 The polynomial f(x)= ar +7x²-9x+b is divisible by 2r-1. The remainder when f(x) is divided by x-2 is 5 times the remainder when f(x) is divided by x + 1. (i) Show that a = 6 and find the value of b. (ii) Using the values from part (i), show that f(x) = (2x − 1)(cx² + dx + e), where c, d and e are integers to be found. (iii) Hence factorise f(x) completely. ICS CamScanner로 스캔하기 KS VENT
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