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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
7 2 1 4 −5 −14
↓ 2 12
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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