JAMB 1998 · UME · Q15

Polynomials & algebraic division

Divide $2x^3 + 11x^2 + 17x + 6$ by $2x + 1$ .

Worked solution (try it first)

Long division: $2x^3 \div 2x = x^2$ .
Subtract $x^2(2x + 1) = 2x^3 + x^2$ to leave $10x^2 + 17x + 6$ .
$10x^2 \div 2x = 5x$ .
Subtract $5x(2x + 1) = 10x^2 + 5x$ to leave $12x + 6$ .
$12x \div 2x = 6$ , and $6(2x + 1) = 12x + 6$ leaves 0.
So the quotient is $x^2 + 5x + 6$ , option A.

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