How do you find all the zeros of # f(x)=x^3+x^2-5x+3#?

1 Answer
May 19, 2016

Answer:

#x^3+x^2-5x+3 = (x-1)(x-1)(x+3)#

Explanation:

#f(x) = x^3+x^2-5x+3#

First note that the sum of the coefficients is #0#. That is:

#1+1-5+3 = 0#

So #x=1# is a zero of #f(x)# and #(x-1)# a factor:

#x^3+x^2-5x+3 = (x-1)(x^2+2x-3)#

Again note that the sum of the coefficients of #x^2+2x-3# is #0#, so there is another factor #(x-1)#

#x^2+2x-3 = (x-1)(x+3)#

Putting it all together:

#x^3+x^2-5x+3 = (x-1)(x-1)(x+3)#