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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