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Question
Using the Remainder Theorem, factorise completely the following polynomial:
3x2 + 2x2 – 19x + 6
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Solution
Let f(x) = 3x2 + 2x2 – 19x + 6
Using hit and trial method,
f(1) = 3 + 2 – 19 + 6 ≠ 0
f(−1) =–3 + 2 + 19 + 6 ≠ 0
f(2) = 24 + 8 – 38 + 6 = 0
Hence, (x – 2) is a factor of f(x)
To factorise 3x2 + 8x − 3
= 3x2 + 9x − x − 3
= 3x(x + 3) −1(x + 3)
= (3x − 1)(x + 3)
Hence 3x3 + 2x3 −19x + 6 = (x − 2)(3x − 1)(x + 3)
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