Find all rational zeros of the polynomial.

Question

Find all rational zeros of the polynomial. (Enter your answers as a comma-separated list. Enter all answers including repetitions.)

P(x) = x⁵ − 6x⁴ − x³ + 34x² − 12x − 40

Answer 1

The math way to do this is to try all factors of 40/1: +/- (1,2,4,5,8,10,20,40) in order to find the only possible rational roots .( -1, -2, 2, 5 (2 is double))

You use synthetic division or regular to lower the order of the equation (which will lower the number of possible roots.

Faster is to use desmos.com and plug in y= P(x) and the zeros are obvious and you can click on the points on the x axis.