Question

(3x+5) is a factor of the polynomial (a-1)x^3 + (a+1)x^2 - (2a + 1)x - 15. Find the value of 'a'. For this value of 'a', factorize the given expression completely.

Answer 1

a = 4

Explanation:

(3x+5) is a factor of the polynomial (a-1)x³ + (a+1)x² - (2a + 1)x - 15

Means x = -5/3 is a root

(a-1)(-5/3)³ + (a+1)(-5/3)² - (2a + 1)(-5/3) - 15 = 0

-125a/27 + 125/27 + 25a/9 + 25/9 + 10a/3 + 5/3 - 15 = 0

a(-125/27 + 25/9 + 10/3) = 15 - 5/3 - 25/9 - 125/27

a(40/27) = 160/27

a = 4

Answer 2

(3x + 5)(x + √3)(x - √3)