Stitz-Zeager_College_Algebra_e-book

# 1 1 2 4 1 6 3 2 2 3 3 2 2 3 3 0 2 0 3 2 0 3 0 success

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Unformatted text preview: replace the −2 in the divisor by 2. Furthermore, the coeﬃcients of the quotient polynomial match the coeﬃcients of the ﬁrst three terms in the last row, so we now take the plunge and write only the coeﬃcients of the terms to get 2 1 4 −5 −14 2 12 14 16 7 0 200 Polynomial Functions We have constructed is the synthetic division tableau for this polynomial division problem. Let’s re-work our division problem using this tableau to see how it greatly streamlines the division process. To divide x3 + 4x2 − 5x − 14 by x − 2, we write 2 in the place of the divisor and the coeﬃcients of x3 + 4x2 − 5x − 14 in for the dividend. Then ‘bring down’ the ﬁrst coeﬃcient of the dividend. 2 1 4 −5 −14 2 1 4 −5 −14 ↓ 1 Next, take the 2 from the divisor and multiply by the 1 that was ‘brought down’ to get 2. Write this underneath the 4, then add to get 6. 2 1 4 −5 −14 ↓2 1 2 1 4 −5 −14 ↓2 16 Now take the 2 from the divisor times the 6 to get 12, and add it to the −5 to get 7. 2 1 4 −5 −14 ↓ 2 12 16 2 1 4 −5 −14 ↓ 2 12 16 7 Finally, take the 2...
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