If f(x) = 4x\(^3\) + px\(^2\) + 7x - 23 is divided by (2x -5), the remainder is 7. find the value of p
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Correct Answer: Option B
Explanation:
f(x) = 4x\(^3\) + px\(^2\) + 7x - 23
If f(x) is divided by (2x -5), the remainder is f(\(\frac{5}{2}\))
f\(\frac{5}{2}\) = 4\(\frac{5}{2}\)\(^3\) + p\(\frac{5}{2}\)\(^2\) + 7\(\frac{5}{2}\) - 23
Hence;
= \(\frac{125}{8}\) + \(\frac{25}{4}\) p + \(\frac{35}{2}\) - 23
28 = 250 + 250p + 70 - 92
25p = -200; p = -8.0
f(x) = 4x\(^3\) + px\(^2\) + 7x - 23
If f(x) is divided by (2x -5), the remainder is f(\(\frac{5}{2}\))
f\(\frac{5}{2}\) = 4\(\frac{5}{2}\)\(^3\) + p\(\frac{5}{2}\)\(^2\) + 7\(\frac{5}{2}\) - 23
Hence;
= \(\frac{125}{8}\) + \(\frac{25}{4}\) p + \(\frac{35}{2}\) - 23
28 = 250 + 250p + 70 - 92
25p = -200; p = -8.0