What are all the possible rational zeros for f(x)x3 8x 6 What is 3f(x 2) if f(x)x3 2x2-4?

Answer 1

To find the possible rational zeros for the polynomial ( f(x) = x^3 + 8x + 6 ), we can use the Rational Root Theorem, which suggests that any rational zero is of the form ( \pm \frac{p}{q} ), where ( p ) is a factor of the constant term (6) and ( q ) is a factor of the leading coefficient (1). The possible rational zeros are ( \pm 1, \pm 2, \pm 3, \pm 6 ).

For ( 3f(x - 2) ) where ( f(x) = x^3 + 2x^2 - 4 ), we first evaluate ( f(x - 2) = (x - 2)^3 + 2(x - 2)^2 - 4 ) and then multiply the result by 3. The expansion would yield ( 3[(x - 2)^3 + 2(x - 2)^2 - 4] ).