Question

Find a polynomial function of degree 3 such that f (2) = 24 and x– 1, x and x+ 2

Answer 1

f(x) = 3x³ + 3x² - 6x

given the factors of the polynomial , then

f(x) =ax(x - 1)(x + 2) ( a is a multiplier )

to find a use f(2) = 24

f(2) = 2a(1)(4) = 24 ⇒8a = 24 ⇒ a = 3, thus

f(x) = 3x(x² + x - 2) = 3x³ + 3x² - 6x