Getting More Involved93.WritingWhat is the difference between the equations(x5)2x210x25 and (x5)2x225?94.WritingIs it possible to square a sum or a difference withoutusing the rules presented in this section? Why should youlearn the rules given in this section?In This SectionU1VDividing Monomials U2VDividing a Polynomial by aMonomialU3VDividing a Polynomial by aBinomial4.8Division of PolynomialsYou multiplied polynomials in Section 4.5. In this section, you will learn to dividepolynomials.U1VDividing MonomialsWe actually divided some monomials in Section 4.1 using the quotient rule for expo-nents. We use the quotient rule here also. In Section 4.2, we divided expressions withpositive and negative exponents. Since monomials and polynomials have nonnegativeexponents only, we will not be using negative exponents here. E X A M P L E 1Dividing monomialsFind each quotient. All variables represent nonzero real numbers.a)(12x5)(3x2)b)24xx33c)120aa22bb24Solutiona)12x5(3x2) 132xx254x524x3The quotient is 4x3. Use the definition of division to check that 4x33x212x5.b)24xx332x332x02 1 2The quotient is 2. Use the definition of division to check that 2 2x34x3.c)120aa23bb245a32b425ab2The quotient is 5ab2. Check that 5ab2(2a2b2)10a3b4.Now do Exercises 1–18If abc, then ais called the dividend,bis called the divisor, and cis called thequotient.We use these terms with division of real numbers or division of polynomials. U2VDividing a Polynomial by a MonomialWe divided some simple polynomials by monomials in Chapter 1 using the distributiveproperty. Now that we have the rules of exponents, we can use them to divide polyno-mials of higher degrees by monomials. Because of the distributive property, each termof the polynomial in the numerator is divided by the monomial from the denominator.