Exam Questions & Step-by-Step Markschemes (5 Problems)
Question 1 • 2024
4 Marks
Using the Factor Theorem, show that (x - 2) is a factor of P(x) = 2x^3 + x^2 - 13x + 6 . Hence, factorize P(x) completely.
Answer: P(x) = (x - 2)(2x - 1)(x + 3)
Question 2 • 2023
4 Marks
When a polynomial f(x) = 2x^3 + ax^2 + bx - 6 is divided by (x - 1) , the remainder is 0 , and when divided by (x + 2) , the remainder is -12 . (i) Find the values of the constants a and b . (ii) Hence, factorise f(x) completely into linear factors.
Answer: a = 3, \quad b = 1, \quad f(x) = (x - 1)(2x^2 + 5x + 6)
Question 3 • 2024
3 Marks
Using remainder and factor theorem, factorize completely: 2x^3 + x^2 - 13x + 6 .
Answer: (x - 2)(2x - 1)(x + 3)
Question 4 • 2023
4 Marks
If (x - 2) and (x + 3) are factors of the polynomial x^3 + ax^2 + bx - 30 , find the values of a and b . Hence, factorize the polynomial completely.
Answer: a = 6, \quad b = -1, \quad \text{Factors: } (x - 2)(x + 3)(x + 5)
Question 5 • 2024
4 Marks
Using the Remainder and Factor Theorem, factorise completely the polynomial: P(x) = 2x^3 + 3x^2 - 11x - 6
Answer: P(x) = (x - 2)(x + 3)(2x + 1)