NumericalModerate3 marks
Use Remainder theorem to factorize the following polynomial : 2x³ + 3x² - 9x - 10
Topic: Remainder and factor theorem
Previous-year question practice database
Answer
Solution diagram
Exam answer
Let f(x) = 2x³ + 3x² − 9x − 10. f(2) = 2(2³) + 3(2²) − 9(2) − 10 = 16 + 12 − 18 − 10 = 0. ∴ (x − 2) is a factor.
Dividing by (x − 2): 2x³ + 3x² − 9x − 10 = (x − 2)(2x² + 7x + 5) = (x − 2)(2x + 5)(x + 1).
Answer: (x − 2)(2x + 5)(x + 1).
Explanation
By the Factor Theorem, f(2)=0 implies (x−2) is a factor. Divide by (x−2), then factor 2x²+7x+5=(2x+5)(x+1).
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