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Show that (x+4),(x-3) and (x-7) are factors of x3 - 6x2 - 19x + 84. |
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Answer» Let f (x) = x3 - 6x2 - 19x + 84 be the given polynomial. In order to prove that (x + 4), (x – 3) and (x – 7) are factors of f (x), it is sufficient to prove that f (-4) = 0, f (3) = 0 and f (7) = 0 respectively. Now, f (x) = x3 - 6x2 - 19x + 84 f (-4) = (-4)3 – 6 (-4)2 – 19 (-4) + 84 = -64 – 96 + 76 + 84 = 0 f (3) = (3)3 – 6 (3)2 – 19 (3) + 84 = 27 – 54 – 57 + 84 = 0 f (7) = (7)3 – 6 (7)2 – 19 (7) + 84 = 343 – 294 – 133 + 84 = 0 Hence, (x – 4), (x – 3) and (x -7) are the factors of the given polynomial x3 - 6x2 - 19x + 84. |
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