What is the factor of this and its root

Question

0=5x^4 - 3x^5 - 2.... i really need help

Answer 1

The equation is  0 = 5x⁴ - 3x⁵ - 2  

Rewrite the equation is  - 3x⁵+ 5x⁴  - 2  = 0

If p/q is a rational zero, then p is a factor of - 2 and q is a factor of - 3.

The possible values of p are   ± 1,   ± 2.

The possible values for q are ± 1 and   ± 3.

So, p/q = ± 1,   ± 2,   ±1/3,   ± 2/3

Make a table for the synthetic division and test possible real zeros.

p/q	-3	5	0	0	0	- 2
-1	-3	8	-8	8	-8	6
1	-3	2	2	2	2	0

Since f(1) =  0,   x  =  1 is a zero. The depressed polynomial is  -3x⁴ + 2x³ + 2x² + 2x + 2 = 0

(x - 1) is a one factor.

Factoring of 5x⁴ - 3x⁵ - 2   = (x -1)(-3x⁴ + 2x³ + 2x² + 2x + 2)