Precal Question

Question

Find all real roots of the given polynomials, using the quadratic formula if necessary. Then write the polynomial in factored form: f(x) = x^3 − 5x^2 + 2x + 12.

FULL STEP BY STEP PLEASE

Answer 1

x-3 is one factor

divide it into the give cubic gives x^2 -2x + 4

x^2 -2x + 1 = -4 + 1 = -3

(x-1)^2 = -3

x-1 = + or - sqr(-3) = + or - isqr3

the other 2 factors are x-isqr3 and x+isqr3

or (x-1.732i)(x+1.732i)(x-3) as the 3 factors