Question

Find the value of all so that the polynomial x3-ax2+13x+15,when divided by x-1,gives 2 as the remainder

Answer 1

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${x}^{3} - a {x}^{2} + 13x + 15 = f(x) \\ x - 1 = g(x) \\ f(x) \div g(x) = q + 2 \\g( x ) = 0 \: \\ so \: \: x = 1 \\ 1 - a + 13 + 15 = 2 \\ 29 - a = 2 \\ - a = 2 - 29 \\ a = 27$
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