Find rational zero of the polynomial 3x4 plus 26x3 plus 91x2 plus 128x plus 52?

Answer 1

To be rational, the numerator has to be a factor of 52 (the last term), and the denominator has to be a factor of 3 (the coefficient of the first term). Try all the combinations, including negative numbers (52/1, -52/1, 52/3, -52/3, 26/1, 26/3, etc.), to see whether one of them is a zero.