SOLUTION: Please help with the equations. Find all of the real zeros of the polynomial function, then use the real zeros to factor f over the real numbers. f(x) = 3x^4 - 6x^3 + 4x^2 -

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please help with the equations. Find all of the real zeros of the polynomial function, then use the real zeros to factor f over the real numbers. f(x) = 3x^4 - 6x^3 + 4x^2 -       Log On


   

Question 616625: Please help with the equations.
Find all of the real zeros of the polynomial function, then use the real zeros to factor f over the real numbers.
f(x) = 3x^4 - 6x^3 + 4x^2 - 2x + 1
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi, 

Find all of the real zeros of the polynomial function

f(x) = 3x^4 - 6x^3 + 4x^2 - 2x + 1   Note: x = 1 is a zero: 3-6+4-2+1 = 0

using synthetic division

1	3	-6	4	-2	1

		3	-3	1	-1

	3	-3	1	-1	0

(x-1)(3x^3 - 3x^2 + x-1)  Note: x = 1 is a zero of 3x^3 - 3x^2 + x-1

using synthetic division

1	3	-3	1	-1	

		3	0	1	

	3	0	1	0

(x-1)(x-1)(3x^2 - 1)

Real zeros is x = 1