The polynomial p(x) = ax³ + bx²-19x+4, where a and b are constants, has a factor x+4 at such that 2p(1) = 5p (0). (a) Show that p(x) = (x+4) (Ax² + Bx+C), where A, B and C are integers to be found.

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03-12-2022
Mathematics

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The polynomial p(x) = ax³ + bx²-19x+4, where a and b are constants, has a factor x+4 at such that 2p(1) = 5p (0). (a) Show that p(x) = (x+4) (Ax² + Bx+C), where A, B and C are integers to be found.

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The polynomial p(x) = ax³ + bx²-19x+4, where a and b are constants, has a factor x+4 at such that 2p(1) = 5p (0). (a) Show that p(x) = (x+4) (Ax² + Bx+C), where A, B and C are integers to be found.​

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The polynomial p(x) = ax³ + bx²-19x+4, where a and b are constants, has a factor x+4 at such that 2p(1) = 5p (0). (a) Show that p(x) = (x+4) (Ax² + Bx+C), where A, B and C are integers to be found.