1 The polynomial p(x) = ax + bx²-3x -4 has a factor of 2x-1 and leaves a remainder of -10 when divided by x + 2. (i) Show that a = 10 and find the value of b. (ii) Given that p(x) = (2x - 1)(x² + sx+t), find the value of each of the integers r, s anc (iii) Hence find the exact solutions of p(x) = 0. VE

Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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PAPER 1
5. FACTORS OF POLYNOMIALS
page 25
F2015
1
The polynomial p(x) = ax³ + bx²-3x-4 has a factor of 2x-1 and leaves a remainder
of 10 when divided by x + 2.
(i) Show that a = 10 and find the value of b.
(ii) Given that p(x) = (2x - 1)(x² +sx+t), find the value of each of the integers r, s and t.
(iii) Hence find the exact solutions of p(x) = 0.
2 AEL
KS VEN
Transcribed Image Text:PAPER 1 5. FACTORS OF POLYNOMIALS page 25 F2015 1 The polynomial p(x) = ax³ + bx²-3x-4 has a factor of 2x-1 and leaves a remainder of 10 when divided by x + 2. (i) Show that a = 10 and find the value of b. (ii) Given that p(x) = (2x - 1)(x² +sx+t), find the value of each of the integers r, s and t. (iii) Hence find the exact solutions of p(x) = 0. 2 AEL KS VEN
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