Use synthetic substitution to find f(2) and f(-1) for each function.
1. f(x) x^2 + 6x +5 21, 0
Answers
Answer:
here is your answer
Step-by-step explanation:
Here are the steps required for Evaluating a Polynomial Using Synthetic Division and the Remainder Theorem:
Step 1 : Step up the synthetic division problem. First, put the number you wan to evaluate in the division box. Next, make sure the polynomial is written in descending order and if any terms are missing you must use a zero to fill in the missing term, finally list only the coefficient in the division problem.
Step 2 : Do the synthetic division. Click here to review the steps required for synthetic division.
Step 3 : Apply the Remainder Theorem, which says, “If a polynomial f(x) is divided by x – c, then the remainder is f(c).” Simply put, the Remainder Theorem says if you want to evaluate a polynomial at some value c, then the answer is the remainder.
Example 1 – Use synthetic division and the Remainder Theorem to find f(3) if f(x) = x3 – 5x2 + 3x + 7.
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 1
Step 2: Do the synthetic division.
Step 2
Step 3: Apply the Remainder Theorem. In this case, the remainder is –2, so the answer is:
Step 3
Example 2 – Use synthetic division and the Remainder Theorem to find f(–2) if f(x) = 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 1
Step 2: Do the synthetic division.
Step 2
Step 3: Apply the Remainder Theorem. In this case, the remainder is –2, so the answer is:
Step 3
Click Here for Practice Problems
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 1
Step 2: Do the synthetic division.
Step 2
Step 3: Apply the Remainder Theorem. In this case, the remainder is –5, so the answer is:
Step 3
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 1
Step 2: Do the synthetic division.
Step 2
Step 3: Apply the Remainder Theorem. In this case, the remainder is 4, so the answer is:
Step 3Here are the steps required for Evaluating a Polynomial Using Synthetic Division and the Remainder Theorem:
Step 1 : Step up the synthetic division problem. First, put the number you wan to evaluate in the division box. Next, make sure the polynomial is written in descending order and if any terms are missing you must use a zero to fill in the missing term, finally list only the coefficient in the division problem.
Step 2 : Do the synthetic division. Click here to review the steps required for synthetic division.
Step 3 : Apply the Remainder Theorem, which says, “If a polynomial f(x) is divided by x – c, then the remainder is f(c).” Simply put, the Remainder Theorem says if you want to evaluate a polynomial at some value c, then the answer is the remainder.
Example 1 – Use synthetic division and the Remainder Theorem to find f(3) if f(x) = x3 – 5x2 + 3x + 7.
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 1
Step 2: Do the synthetic division.
Step 2
Step 3: Apply the Remainder Theorem. In this case, the remainder is –2, so the answer is:
Step 3
Example 2 – Use synthetic division and the Remainder Theorem to find f(–2) if f(x) = 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 1
Step 2: Do the synthetic division.
Step 2
Step 3: Apply the Remainder Theorem. In this case, the remainder is –2, so the answer is:
Step 3
Click Here for Practice Problems
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 1
Step 2: Do the synthetic division.
Step 2
Step 3: Apply the Remainder Theorem. In this case, the remainder is –5, so the answer is:
Step 3
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 1
Step 2: Do the synthetic division.
Step 2
Step 3: Apply the Remainder Theorem. In this case, the remainder is 4, so the answer is:
Step 3
Answer:
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