If we divide by $x-1$, the remainder is?
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Ref: R6790

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Solution

When \[1 + 3x + 5x^2 + 7x^3 + \dots + 99x^{49}\] is divided by $x-1$ the remainder is

$2000$,
$2500$,
$3000$,
$3500$.

The remainder theorem tells us that when a polynomial $p(x)$ is divided by $x-1$ then the remainder is $p(1)$, which in this case is \[1 + 3 + 5 + 7 + \dots + 99.\] This is an arithmetic progression, and so sums to \[\frac{1}{2}\times 50(1+99) = 2500\] and the answer is (b).

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Polynomials & Rational Functions

If we divide by $x-1$, the remainder is? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

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If we divide by $x-1$, the remainder is?
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