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Unformatted text preview: in the divisor times the 7 to get 14, and add it to the −14 to get 0. 2 1 4 −5 −14 ↓ 2 12 14 16 7 2 1 4 −5 −14 ↓ 2 12 14 16 7 0 The first three numbers in the last row of our tableau are the coefficients of the quotient polynomial. Remember, we started with a third degree polynomial and divided by a first degree polynomial, so the quotient is a second degree polynomial. Hence the quotient is x2 + 6x + 7. The number in the box is the remainder. Synthetic division is our tool of choice for dividing polynomials by divisors of the form x − c. It is important to note that it works only for these kinds of divisors.5 Also take note that when a polynomial (of degree at least 1) is divided by x − c, the result will be a polynomial of exactly one less degree. Finally, it is worth the time to trace each step in synthetic division back to its corresponding step in long division. While the authors have done their best to indicate where the algorithm comes from, there is no subst...
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