Final answer:
To factor the polynomial x^4 -3x^3 + 4x^2 - 6x + 4 using synthetic division, we can use the Rational Root Theorem to find possible rational roots. By trying out the possible roots using synthetic division, we find that x = 1 is a root of the polynomial. The factored form of the polynomial is (x-1)(x^3-2x^2+2x-4).
Step-by-step explanation:
To factor the polynomial using synthetic division, we can use the Rational Root Theorem to find possible rational roots. The possible rational roots of the polynomial are the factors of the constant term, which is 4, divided by the factors of the leading coefficient, which is 1.
By trying out the possible roots and using synthetic division, we can see that x = 1 is a root of the polynomial. We then divide the polynomial by (x-1) using synthetic division to find the other factor.
The factored form of the polynomial is (x-1)(x^3-2x^2+2x-4). Therefore, the polynomial x^4 -3x^3 + 4x^2 - 6x + 4 = 0 can be factored as (x-1)(x^3-2x^2+2x-4) = 0.