Question

What is the expanded form of the polynomial p(x) = (x - 1)(x - 2)(x - 3)(x - 4)?

Answer 1

The expanded form of the polynomial p(x) = (x - 1)(x - 2)(x - 3)(x - 4) is x^4 - 10x^3 + 35x^2 - 50x + 24.

Step-by-step explanation:

The expanded form of the polynomial p(x) = (x - 1)(x - 2)(x - 3)(x - 4) can be found by multiplying the binomials together. The expanded form of the polynomial p(x) = (x - 1)(x - 2)(x - 3)(x - 4) is x^4 - 10x^3 + 35x^2 - 50x + 24.

Here are the steps:

1. Multiply the first two binomials: (x - 1)(x - 2) = x^2 - 3x + 2
2. Multiply the result from step 1 by the third binomial: (x^2 - 3x + 2)(x - 3) = x^3 - 6x^2 + 11x - 6
3. Multiply the result from step 2 by the fourth binomial: (x^3 - 6x^2 + 11x - 6)(x - 4) = x^4 - 10x^3 + 35x^2 - 50x + 24

Therefore, the expanded form of the given polynomial is x^4 - 10x^3 + 35x^2 - 50x + 24.