Answer:
2x3 + 3x2 – 3x + 4.
Step 1: Step up the synthetic division problem. In this case, we are trying to evaluate f(3), so put 3 in the division box.
Step 2: Do the synthetic division.
Step 3: Apply the Remainder Theorem. In this case, the remainder is –2, so the answer is:
Example 3 – Use synthetic division and the Remainder Theorem to find f(2) if f(x) = –x3 + 5x – 7.
Step 1: Step up the synthetic division problem. In this case, we are trying to evaluate f(2), so put 2 in the division box.
Step 3: Apply the Remainder Theorem. In this case, the remainder is –5, so the answer is:
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Example 4 – Use synthetic division and the Remainder Theorem to find f(–1) if f(x) = 2x4 – 3x2 + 5.
Step 1: Step up the synthetic division problem. In this case, we are trying to evaluate f(–1), so put –1 in the division box.
Step 3: Apply the Remainder Theorem. In this case, the remainder is 4, so the answers.
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Answer:
2x3 + 3x2 – 3x + 4.
Step 1: Step up the synthetic division problem. In this case, we are trying to evaluate f(3), so put 3 in the division box.
Step 2: Do the synthetic division.
Step 3: Apply the Remainder Theorem. In this case, the remainder is –2, so the answer is:
Example 3 – Use synthetic division and the Remainder Theorem to find f(2) if f(x) = –x3 + 5x – 7.
Step 1: Step up the synthetic division problem. In this case, we are trying to evaluate f(2), so put 2 in the division box.
Step 2: Do the synthetic division.
Step 3: Apply the Remainder Theorem. In this case, the remainder is –5, so the answer is:
Click Here for Practice Problems
Example 4 – Use synthetic division and the Remainder Theorem to find f(–1) if f(x) = 2x4 – 3x2 + 5.
Step 1: Step up the synthetic division problem. In this case, we are trying to evaluate f(–1), so put –1 in the division box.
Step 2: Do the synthetic division.
Step 3: Apply the Remainder Theorem. In this case, the remainder is 4, so the answers.