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Which binomial is NOT a factor of the expression x 3 – 11x 2 + 16x + 84? [1] x-5 [2] 2x-6 [3] x+7 |
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Answer» It's much easier to check if a GIVEN polynomial is a factor than it is to entirely factor it.For example, you can always do polynomial long division and check if the remainder is zero. For the special case of linear FACTORS x - a, you can do synthetic division (before anyone says anything, yes, I know that there's a form of synthetic division for higher degree divisors, but it's not commonly taught).Another approach is the rational root theorem. For ax + b to be a factor of a polynomial, with a and b both integers, it's necessary (but not sufficient) for a to be a factor of the LEADING term of the polynomial and for b to be a factor of the constant term. So that WOULD rule out a factor like 2x - 9, since 9 isn't a factor of 84. |
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