Remainder Theorem
Question
Find the remainder when \(x^2 - 2x - 3\) is divided by \(x + 1\) using the Remainder Theorem
Solution
Show solution Hide solution Fully worked — 4 steps
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Set up the function and the value to substitute
Let \(f(x) = x^2 - 2x - 3\). The divisor is \(x + 1\), so we evaluate at \(x = -1\). By the Remainder Theorem, the value of \(f(-1)\) is the remainder.
\[ f(x) = x^2 - 2x - 3 \] -
Substitute \(x = -1\) into \(f(x)\)\[ f(-1) = (-1)^2 - 2(-1) - 3 \]
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Solve for \(f(-1)\)\[ f(-1) = 1 + 2 - 3 = 0 \]
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Final answer
That is, the remainder is 0.
\[ f(-1) = 0 \]