NumericalHard4 marks
The polynomial 3x³ + 8x² - 15x + k has (x - 1) as a factor. Find the value of k. Hence factorize the resulting polynomial completely.
Topic: Remainder and factor theorem
Previous-year question practice database
Answer
Exam answer
k = 4; polynomial = (x−1)(3x−1)(x+4).
Explanation
Factor Theorem: f(1)=0 gives k=4. Divide by x−1 and factor the quadratic.
More from Factorization of Polynomials (Remainder and Factor Theorems)
What must be added to x³ + 7x² + 3x + 2 so that the result is completely divisible by (x + 2)?2026Find the value of k.2026Using the value of k factorise completely the polynomial kx³ + 3x² − 11x − 62026The factor common to the two polynomials x² - 4 and x³ - x² - 4x + 42025the value of ‘k’.2025hence, factorise the resulting polynomial completely.2025