NumericalModerate3 marks
Use factor theorem to factorise 6x³ + 17x² + 4x - 12 completely.
Topic: Remainder and factor theorem
Previous-year question practice database
Answer
Solution diagram
Exam answer
Let f(x)=6x³+17x²+4x−12.
f(−2) = 6(−8)+17(4)+4(−2)−12 = −48+68−8−12 = 0.
So (x+2) is a factor.
Dividing: 6x³+17x²+4x−12 = (x+2)(6x²+5x−6).
Factor the quadratic: 6x²+5x−6 = (2x+3)(3x−2).
Answer:
(x+2)(2x+3)(3x−2).
Explanation
Use the Factor Theorem to identify x+2 as a factor, then factor the remaining quadratic.
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