How do you list all possible roots and find all factors and zeroes of #5x^3+29x^2+19x-5#?
1 Answer
Jun 23, 2016
with zeros
Explanation:
#f(x) = 5x^3+29x^2+19x-5#
Note that if you reverse the signs on the terms of odd degree then the sum of the coefficients is
That is:
Hence
#5x^3+29x^2+19x-5 = (x+1)(5x^2+24x-5)#
To factor the remaining quadratic use an AC method:
Look for a pair of factors of
The pair
Use this pair to split the middle term and factor by grouping:
#5x^2+24x-5#
#=5x^2+25x-x-5#
#=(5x^2+25x)-(x+5)#
#=5x(x+5)-1(x+5)#
#=(5x-1)(x+5)#
Hence zeros