Question

factorize x3 + 3x2 - 13x -15 into linear factors​

Answer 1

Answer:

et p(x) = x3 + 3x2 – 13x – 15 Sum of all the co-efficients = 1 + 3 – 13 – 15 = -24 + 0 Hence x – 1 is not a factor Sum of co-efficients of even powers with constant = 3 – 15 = – 12 Sum of coefficients of odd powers = 1 – 13 = – 12 Hence x + 1 is a factor of p(x) Now use synthetic division to find the other factors. Hence p(x) = (x + 1) (x2 + 2x – 15) Now x3 + 3x2 – 13x – 15 = (x + 1)(x2 + 2x – 15) Now x2 + 2x – 15 = x2 + 5x – 3x – 15 = x(x + 5) – 3 (x + 5) = (x + 5)(x – 3) Hence x3 + 3x2 – 13x – 15 = (x + 1)(x + 5)(x – 3)Read more on Sarthaks.com - https://www.sarthaks.com/967178/factorize-x-3-3x-2-13x-15?show=967192#a967192