What is the value of the polynomial p(x) = 3x^2 - 2x + 1 at x = 2?

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Question: What is the value of the polynomial p(x) = 3x^2 - 2x + 1 at x = 2?

Options:

Correct Answer: 9

Solution:

Substituting x = 2 into the polynomial gives p(2) = 3(2^2) - 2(2) + 1 = 12 - 4 + 1 = 9.

What is the value of the polynomial p(x) = 3x^2 - 2x + 1 at x = 2?

What is the value of the polynomial p(x) = 3x^2 - 2x + 1 at x = 2?

Step 1: Identify the polynomial p(x) = 3x^2 - 2x + 1.
Step 2: Substitute x = 2 into the polynomial. This means we replace every x in the polynomial with 2.
Step 3: Calculate 2^2, which is 4.
Step 4: Multiply 3 by 4 (from Step 3) to get 12.
Step 5: Calculate -2 times 2, which is -4.
Step 6: Now, add the results from Steps 4 and 5 with the constant term 1: 12 - 4 + 1.
Step 7: First, do 12 - 4, which equals 8.
Step 8: Then, add 1 to 8, which gives you 9.
Step 9: The final result is p(2) = 9.

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