Question

24. What must be added to 2x4 – 5x + 2x²-x-3 so that the result is exactly
divisible by (x - 2)?
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Answer 1

Answer:

$Let \: \: the \: \: required \: \: number \: \: to \: \: be \: \: added \: \: be \: \: \bold{k}. \\ Then , \\ \\ p(x) = 2 {x}^{4} - 5 {x}^{3} + 2 {x}^{2} - x - 3 + k \\ \\ g(x) = x - 2 = 0 \\ \boxed{x = \underline{ \underline{2}}} \\ \\ p(x) = 2 {x}^{4} - 5 {x}^{3} + 2 {x}^{2} - x - 3 + k = 0\\ = 2 {(2)}^{4} - 5 {(2)}^{3} + 2 {(2)}^{2} - 2 - 3 + k = 0 \\ = (2 \times 16) - (5 \times 8) + (2 \times 4) - 2 - 3 + k = 0\\ = 32 - 40 + 8 - 2 - 3 + k = 0 \\ = - 5 + k = 0\\ \boxed{k = \underline{ \underline{5}}}$