Identify the polynomial and the divisor.

Question

ScanSolve AI Tutor · Accepted Answer

Step 1: Identify the polynomial and the divisor. The polynomial is f(x) = x⁴ − 2x³ − 6x² − 2x + 1. The divisor is x+2. Step 2: Apply the Remainder Theorem. The Remainder Theorem states that if a polynomial f(x) is divided by x−a, the remainder is f(a). In this case, the divisor is x+2, which can be written as x − (−2). So, a = −2. Therefore, the remainder is f(−2). Step 3: Substitute x = −2 into the polynomial f(x). f(−2) = (−2)⁴ − 2(−2)³ − 6(−2)² − 2(−2) + 1 Step 4: Calculate each term. (−2)⁴ = 16; −2(−2)³ = −2(−8) = 16; −6(−2)² = −6(4) = −24; −2(−2) = 4 +1 Step 5: Sum the calculated terms to find the remainder. f(−2) = 16 + 16 − 24 + 4 + 1; f(−2) = 32 − 24 + 4 + 1; f(−2) = 8 + 4 + 1; f(−2) = 13 The remainder is 13. The final answer is 13.

Identify the polynomial and the divisor.

Answer

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