Question

find the value of m so that 2x - 1 be a factor of 8x4 + 4x3 -16x2 + 10x + m​

Answer 1

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Answer 2

Answer:

m = -2

Step-by-step explanation:

Suppose f(x) = $8x^{4} + 4x^{3} -16x^{2} + 10x + m$

If  2x - 1  is a factor of given equation then f($\frac{1}{2}$) must be zero

Replace f(x) with f($\frac{1}{2}$)

$f(\frac{1}{2}) = 8(\frac{1}{2})^{4} + 4(\frac{1}{2})^{3} - 16(\frac{1}{2})^{2} + 10(\frac{1}{2}) + m = 0\\  \\8.\frac{1}{16} + 4. \frac{1}{8} - 16.\frac{1}{4} + 10.\frac{1}{2} + m = 0\\\\\frac{1}{2} + \frac{1}{2} - 4 + 5 + m = 0\\\\1 - 4 + 5 + m = 0\\\\m = 4 - 6\\\\m = -2$