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Long Division Method to Divide Two Polynomials

x3+3 x2-4 x-1...

Question

$x^{3} + 3 x^{2} - 4 x - 12$ , when divided by (x - 2), leaves a remainder of $a x^{2} + b x + c$ . Find a, b, c

a = 4 b = 2 c = 8

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a = 12 b = 4 c = 8

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b = 5 a = 1 c = 6

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c = 8 a = 9 b = 4

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Solution

The correct option is C
b = 5 a = 1 c = 6

Quotient = $x^{2}$ + 5x + 6 = $a x^{2}$ + bx + c

$\Rightarrow$ a = 1, b = 5 c = 6

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