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Remainder And Factor Theorems — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsRemainder And Factor Theorems1 Mark
Question
Prove that $(x-3)$ is a factor of $x^3 - x^2 - 9x +9$ and hence factorize it completely.
✓

Answer

If $x - 3$ assumed to be factor, then $x = 3$. Substituting this in problem polynomial, we get:
$f(3) = 3 × 3 × 3 - 3 × 3 - 9 × 3 + 9 = 0$
Hence its proved that $x - 3$ is a factor of the polynomial.

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