Question

Let P(x)=ˣ⁴-4ˣ³+12x-9. Use Rational Root Theorem & the synthetic Division Theorer to factor P(x) completely.

Answer 1

To factor the polynomial P(x) = ˣ⁴-4ˣ³+12x-9 completely, you can use the Rational Root Theorem and Synthetic Division. The factorization of P(x) is (x-1)(x+1)(x-3)(x-4).

Step-by-step explanation:

To factor the polynomial P(x) = ˣ⁴-4ˣ³+12x-9 completely, we can use the Rational Root Theorem and Synthetic Division.

To use the Rational Root Theorem, we need to find all the possible rational roots. The factors of the constant term -9 are ±1, ±3, ±9, and the factors of the leading coefficient 1 are ±1. So the possible rational roots are ±1, ±3, ±9.

We can then use synthetic division to check each of these possible roots. By testing them one by one with synthetic division, we find that the factorization of P(x) is (x-1)(x+1)(x-3)(x-4).