Given that f(x)=2x3 + 3x2 - 5x - 6 and (x+1) is a factor,factorise fully the polynomial f(x).State the set of values of x for which f(x) ≤ 0?
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Given that f(x) = 2x^3 + 3x^2 - 5x - 6 and (x+1) is a factor, factorise fully the polynomial f(x). State the set of values of x for which f(x) ≤ 0
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(2x^3 + 3x^2 - 5x - 6) / (x+1) = 2x^2 + x - 6
(2x^2 + x - 6) / (x+1) = (2x - 3)(x + 2)
f(x) = 0 @ x = -2 ; -1 ; 3/2
Since the coefficient of the highest power term (2x^3) is positive, the curve goes to infinity as x goes to infinity. The curve crosses from negative to positive or vice versa at each zero.
f(x) < 0 @ x < -2 and -1 < x < 3/2
f(x) > 0 @ -2 < x < -1 and 3/2 < x