Question

Use the remainder theorem to find P (1) for P(x)=x^4-3x³+4x-4.

Specifically, give the quotient and the remainder for the associated division and the value of P (1).

Answer 1

Using the Remainder Theorem to evaluate P(1) for the polynomial P(x) = x^4 - 3x^3 + 4x - 4, we simply substitute x with 1, and get P(1) = -2, which is the remainder of the division.

Step-by-step explanation:

To find P(1) for the polynomial P(x) = x^4 - 3x^3 + 4x - 4 using the Remainder Theorem, we simply evaluate the polynomial at x = 1.

The Remainder Theorem states that when a polynomial P(x) is divided by (x - a), the remainder is P(a). In this case, a is 1.

So, P(1) = (1)^4 - 3(1)^3 + 4(1) - 4 = 1 - 3 + 4 - 4 = -2.

The quotient is not explicitly required by the theorem for evaluating P(1), but only the remainder is the value of P(1), which is -2 in this case.