If \((x - 5)\) is a factor of \(x^3 - 4x^2 - 11x + 30\),
FURTHER MATHEMATICS
WAEC 2023
If \((x - 5)\) is a factor of \(x^3 - 4x^2 - 11x + 30\), find the remaining factors.
- A. \((x + 3) and (x - 2)\)
- B. \((x - 3) and (x + 2)\)
- C. \((x - 3) and (x - 2)\)
- D. \((x + 3) and (x + 2)\)
Correct Answer: A. \((x + 3) and (x - 2)\)
Explanation
(x - 5) is a factor of \(x^3 - 4x^2 - 11x + 30\). To find the remaining factors, let's draw out \((x - 5)\) from the parent expression.
\(x^3 - 4x^2 - 11x + 30 = x^3 - 5x^2 + x^2 - 5x - 6x + 30\)
\(= x^2(x - 5) + x(x - 5) - 6(x - 5) = (x - 5)(x^2 + x - 6)\)
∴ To find the remaining factors, we factorize \((x2 + x - 6)\)
\(x^2 + x - 6 = x^2 + 3x - 2x - 6\)
\(= x(x + 3) - 2(x + 3) = (x + 3)(x - 2)\)
∴ The other two factors are \((x + 3) and (x - 2)\)
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