Question

Given f(x) = 2x^3 + ax^2 - 7a^2x - 6a^3, determine whether or not x-a and x+a are factors of f(x). Hence, find, in terms of a, the roots of f(x) = 0.
thankyou so much

Answer 1

Answer:

Step-by-step explanation:

f(x) = 2x³ + ax² - 7a²x - 6a³

= 2x³ - 2a²x + ax² - a³ - 5a²x - 5a³

= 2x(x² - a²) + a(x² - a²) - 5a²(x+a)

= (2x+a)(x - a)(x + a) - 5a²(x + a)

= (x + a)[(2x + a)(x - a) - 5a²]

= (x + a)(2x² - ax - 6a²)

= (x + a)(2x + 3a)(x - 2a)