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Graph the polynomial function. Factor first if the expression is not in factored form. f(x) =...

Graph the polynomial function. Factor first if the expression is not in factored form.

f(x) = x^3 + 7x^2=4x-12

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Answer #1

Graph the polynomial function. Factor first if the expression is not in factored form.

Perhaps the 2nd = sign is a mistake. Then, we have f(x) = x3 + 7x2+4x-12. Now, as per the rational roots theorem, the roots of f(x) are likely to be of the form p/q where p is a factor of -12 and q is a factor of 1. The factors of -12 are ± 1,2,3,4,6,12 and the factors of 1 are ± 1. Further, f(1) = 1+7+4-12 = 0. Hence 1 is a root of f(x) so that (x-1) is a factor of f(x). Then f(x) = (x-1)x2 +8(x-1)x +12(x-1) = (x-1)(x2 +8x+12) = (x-1)(x+6)(x-2).

A grapf off(x) is attached. It may be observed that the graph crosses the X-Axis at x = -6,-2 and 1.

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