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If the polynomial f(x) = x^3 - 3x^2 + 4 is evaluated at x = 1, what is the resul
If the polynomial f(x) = x^3 - 3x^2 + 4 is evaluated at x = 1, what is the result?
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If the polynomial f(x) = x^3 - 3x^2 + 4 is evaluated at x = 1, what is the result?
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Evaluating f(1) gives 1^3 - 3(1^2) + 4 = 1 - 3 + 4 = 2.
Questions & Step-by-step Solutions
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Q: If the polynomial f(x) = x^3 - 3x^2 + 4 is evaluated at x = 1, what is the result?
Solution:
Evaluating f(1) gives 1^3 - 3(1^2) + 4 = 1 - 3 + 4 = 2.
Steps: 8
Show Steps
Step 1: Identify the polynomial function, which is f(x) = x^3 - 3x^2 + 4.
Step 2: Substitute x = 1 into the polynomial. This means we will replace every x in the function with 1.
Step 3: Calculate 1^3. This equals 1.
Step 4: Calculate 3(1^2). First, find 1^2, which is 1, then multiply by 3. This equals 3.
Step 5: Now, substitute these values back into the equation: f(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: The final result of f(1) is 2.
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