JAMB 2017 · UTME (set 2) · Q47

Polynomials & algebraic division

Divide $4x^3 - 3x + 1$ by $2x - 1$ .

Worked solution (try it first)

Write the missing $x^2$ term: $4x^3 + 0x^2 - 3x + 1$ .
Then $4x^3 \div 2x = 2x^2$ .
Subtract $4x^3 - 2x^2$ to leave $2x^2 - 3x + 1$ .
$2x^2 \div 2x = x$ .
Subtract $2x^2 - x$ to leave $-2x + 1$ .
$-2x \div 2x = -1$ , and $-1(2x - 1) = -2x + 1$ leaves 0.
So the quotient is $2x^2 + x - 1$ , option D.

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