two polynomial functions are defined by fx x3 a 3x 26 and gx 3x3 x2 5a
Two polynomial functions are defined by f(x) = x³ + (a – 3)x + 26 and g(x) = 3x3 + x² + 5ax + 4b, where a and b are constants. (a) Given that f(x) and g(x) have a common factor of ( – 2) show that a = -4 and find the value of b. (b) Using the values of a and b, factorise f(x) fully. Hence show that f(x) and g(x) have two common factors.
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