Same topic3 marksDifficulty: Medium
Show that (x − 3) is a factor of x3 − 2x2 − 5x + 6, and hence factorise the polynomial completely.
Factorisation of Polynomials
3 marksDifficulty: Medium
Find the value of a if (x + 2) is a factor of 2x3 + ax2 + 11x + a + 3.
Original Khojo Papers practice question — not from a past board paper.
Answer
a = 7
No citable source has been recorded for this record. Treat it as practice material, not as fact.
Explanation
If (x + 2) is a factor then f(−2) = 0. So 2(−8) + a(4) + 11(−2) + a + 3 = 0, giving −16 + 4a − 22 + a + 3 = 0 and 5a = 35, so a = 7.
Related questions
From the same topic and chapter, at a similar level.
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Find the value of a if (x − 2) is a factor of x3 + ax2 + 2x − 8.
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Show that (x − 3) is a factor of x3 − 2x2 − 5x + 6.
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Same chapter3 marksDifficulty: Medium
Find k if x3 + kx2 − 3x + 6 leaves a remainder of 10 when divided by (x − 2).
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