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Complete the synthetic division problem below 2 1 5

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Concept:

Synthetic division is a shortcut for dividing a polynomial by a binomial of the form x − c.
Use the coefficients of the polynomial and the root c to get the quotient and remainder in a compact table.
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Example:

Divide 2x^2 + x + 5 by x − 2 (c = 2)
– Coefficients: 2 | 1 | 5
– Bring down the leading coefficient: 2
– Multiply by c: 2 × 2 = 4; add to next coefficient: 1 + 4 = 5
– Multiply by c: 5 × 2 = 10; add to next coefficient: 5 + 10 = 15
– Quotient coefficients: 2, 5 → quotient: 2x + 5; remainder: 15
– Result: (2x^2 + x + 5) ÷ (x − 2) = 2x + 5 + 15/(x − 2)

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