Mathematics
Answer
By factor theorem,
If x - a is a factor of polynomial f(x), then remainder f(a) = 0.
Given,
x - 1 is a factor of 8x2 - 7x + m.
⇒ x - 1 = 0
⇒ x = 1.
Substituting x = 1, in x3 - kx2 + 11x - 6 remainder will be zero.
⇒ 13 - k(1)2 + 11(1) - 6 = 0
⇒ 1 - k + 11 - 6 = 0
⇒ 6 - k = 0
⇒ k = 6.
Hence, Option 3 is the correct option.
Related Questions
(3x + 5) is a factor of the polynomial (a - 1)x3 + (a + 1)x2 - (2a + 1)x - 15. Find the value of 'a'. For this value of 'a', factorise the given polynomial completely.
Using remainder theorem, find the value of k if on dividing 2x3 + 3x2 - kx + 5 by (x - 2) leaves a remainder 7.
Find the value of 'a' if x - a is a factor of the polynomial 3x3 + x2 - ax - 81.
While factorizing a given polynomial, using remainder and factor theorem, a student finds that x + 3 is a factor of 2x3 - x2 - 5x - 2.
(a) Is the student's, solution correct stating that (x + 3) is a factor of the given polynomial?
(b) Give a valid reason for your answer.
(c) Factorize the given polynomial completely.