College Algebra
posted by Chama on .
Use the rational zeros theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers.
f(x)=2x^3x^2+2x1

Possible rational zeros:
± 1, ± 1/2
f(1) = 2  1 + 2  1 ≠0
f(1) = 2  1  2  1 ≠0
f(1/2) = 1/4  1/4 + 11 = 0 , yeahh, (2x  1) is a factor
Using long division...
2x^3x^2+2x1 = (2x  1)(x^2 + 1)
so x = 1/2 or x^2 = 1
x = 1/2 or x = ± i
so the only real zero is x=1/2 
How do you use the real zeros to factor f?

if x=a is a real zero. (xa) is a factor. Divide f(x) by (xa) and see what the quotient is. Maybe you can factor it, maybe not. In this case, not.

Ok thank you