For the following find the real zeros of f Use the real zero

For the following, find the real zeros of f. Use the real zeros to factor f. f(x) = x^3 + 3x^2 - 13x- 15 Find the real zero(s) of f. Select the correct choice below and, if necessary; fill in the answer box to complete your answer. A. The real zero(s) of f is/are x =. B. There are no real zeros. Use the real zero(s) to factor f. f(x) =

Solution

f(x) = x^3 +3x^2- 13x -15

To find zeros for polynomials of degree 3 or higher we use Rational Root Test.

The Rational Root Theorem tells you that if the polynomial has a rational zero then it must be a fraction pq, where p is a factor of the trailing constant and q is a factor of the leading coefficient.

The factor of the leading coefficient (1) is 1 .The factors of the constant term (-15) are 1 3 5 15 . Then the Rational Roots Tests yields the following possible solutions:

±11, ±31, ±51, ±151

Substitute the psossible roots one by one into the polynomial to find the actual roots.

P(x), we obtain P(1)=0.

Divide P(x) with x+1: (x^3 +3x^2- 13x -15) /(x+1) =x2+2x15

splve the quadratice: x^2 +2x -15 =0

x^2 +5x -3x -15=0

x(x+5)-3(x+5) =0

(x-3)(x+5)

Roots of f(x) are :x =-1, 3, -5

Factored form : (x+1)(x-3)(x+5)