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Division of Algebraic Expressions - Dividing a Polynomial by a Polynomial

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Dividing a Polynomial by a Polynomial:

In the case of divisions of algebraic expression, we have Dividend = Divisor × Quotient. In general, however, the relation is Dividend = Divisor × Quotient + Remainder Thus, we have considered in the present chapter only those divisions in which the remainder is zero.

Consider (7x2 + 14x) ÷ (x + 2)
We shall factorise (7x2 + 14x) first to check and match factors with the denominator:  
7x2 + 14x = `(7 xx x xx x) + (2 xx 7 xx x)`

                 `= 7 xx x xx (x + 2)`

                  `= 7x(x + 2)`

Now,

`(7x^2 + 14x) ÷ (x + 2) = (7x^2 + 14x)/(x + 2)`

                                       `= (7x(x + 2))/(x + 2)`

                                        = 7x       ......[Cancelling the factors (x + 2)]

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