What is the value of P(1) for the polynomial P(x) = x^3 - 3x^2 + 4?

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Question: What is the value of P(1) for the polynomial P(x) = x^3 - 3x^2 + 4?

Options:

Correct Answer: 2

Solution:

Substituting x = 1 into P(x) gives P(1) = 1^3 - 3(1^2) + 4 = 2.

What is the value of P(1) for the polynomial P(x) = x^3 - 3x^2 + 4?

What is the value of P(1) for the polynomial P(x) = x^3 - 3x^2 + 4?

Step 1: Identify the polynomial P(x) = x^3 - 3x^2 + 4.
Step 2: Substitute x = 1 into the polynomial. This means we will replace every x in P(x) with 1.
Step 3: Calculate 1^3. This equals 1.
Step 4: Calculate 3(1^2). First, find 1^2 which equals 1, then multiply by 3 to get 3.
Step 5: Now, substitute these values into the polynomial: P(1) = 1 - 3 + 4.
Step 6: Perform the subtraction: 1 - 3 equals -2.
Step 7: Now add 4 to -2: -2 + 4 equals 2.
Step 8: Therefore, the value of P(1) is 2.

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