Question

Using the Remainder Theorem, factorise completely the following polynomial: 

3x² + 2x² – 19x + 6

Answer 1

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)