In this section, we shall learn division of polynomials in one and two variables by factorizing the dividend and divisor and then cancelling out the common factors from the zamerator and denominator. Following examples will illustrate the procedure:
Example : Divide
\( a^4 – b^4 by a – b \)
Solution
\( a^4 – b^4 – (a^2)^2 – (b^2)^2 \)
\( a^4 – b^4 = (a^2 – b^2)(a^2 +b^2) \)
\( a^4 – b^4 =(a-b)(a+b)(a^2 + b^2) \)
\( (a^4- b^4) ÷ (a—b) \)
\( a^4-b^4/ a – b \)
\( = (a-b) (a+b) (a^2+B^2)/a-b \)
\( = (a+b) (a^2 + b^2) \)