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41 Rh 3. Multiply the whole divisor by this quotient, and put the product under the dividend.

4. Subtract and bring down from the dividend as many terms as may be necessary.

Repeat these operations till all the terms from the dividend are brought down.

Ex. 1. Divide x^ + 11x + 30 by x + 6.

Arrange the work thus :

x + 6)x^2 + 11x + 30(

divide x^ the first term of the dividend, by x, the first term of the divisor ; the quotient is x. Multiply the whole divisor by x, and put the product x ^ + 6x under the dividend. We then have

x + 6)x^2 + 11x + 30(x x^2+ 6x

by subtraction 5x + 30

On repeating the process above explained we find that the next term in the quotient is x+ 5. The entire operation is more compactly written as follows :

x + 6)x^2 + x + 30(x+ 5 x^2+ 6x 5x + 30 5x + 30

The reason for the rule is this: the dividend may be divided into as many parts as may be convenient, and the complete quotient is found by taking the sum of all the partial quotients. Thus x^2 + 11 x + 30 is divided by the above process into two parts, namely, x^2 - 6 x, and 5 x + 30, and each of these is divided by x+ 6 ; thus we obtain the complete quotient x + 5.

Ex. 2. Divide 24 x^2 - 65 xy + 21 y^2 by 8 x - 3 y.

8 x - 3 y)24 x^2 - 65 xy + 21 y^2( 3x -7y. 24x2- 9xy -56xy + 21y^2 -50xy + 21y^2