NumericalHard4 marks
Find the value of 'a' if x - a is a factor of the polynomial 3x³ + x² - ax - 81.
Topic: Remainder and factor theorem
Previous-year question practice database
Answer
Exam answer
a = 3
Explanation
By the Factor Theorem, substitute x=a into 3x³+x²−ax−81. This gives 3a³−81=0 ⇒ a³=27 ⇒ a=3.
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