Same topic3 marksDifficulty: Medium
Find the value of a if (x + 2) is a factor of 2x3 + ax2 + 11x + a + 3.
Factorisation of Polynomials
3 marksDifficulty: Medium
Show that (x − 3) is a factor of x3 − 2x2 − 5x + 6, and hence factorise the polynomial completely.
Original Khojo Papers practice question — not from a past board paper.
Answer
(x − 3)(x − 1)(x + 2)
No citable source has been recorded for this record. Treat it as practice material, not as fact.
Explanation
f(3) = 27 − 18 − 15 + 6 = 0, so by the factor theorem (x − 3) is a factor. Dividing gives the quotient x2 + x − 2, which factorises as (x + 2)(x − 1). Hence the complete factorisation is (x − 3)(x − 1)(x + 2).
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From the same topic and chapter, at a similar level.
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Show that (x − 3) is a factor of x3 − 2x2 − 5x + 6.
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