Division of a Polynomial by a Binomial

Division of a Polynomial by Binomial While dividing polynomials by binomial, do the following steps Step1:- Write the question in fraction form Step2:- Factorise Polynomial by taking common factors Step3:- Cancel out common factors in both the numerator and denominator Remember your exponent laws for dividing. You subtract the exponents if the base is the same. am = am - n an a5 = a5-3 = a2 a3 For example:

Example 1: Simplify (5x2 + 10x) ÷ (x + 2) Step1:- Write the question in fraction form Step2:- Factorise Polynomial by taking common factors 5 x x x x + 5 x 2 x x ( x + 2) Step3:- Cancel out common factors in both the numerator and denominator Cancelling (x+2) in both numerator and denominator = 5x

Compare with suitable Identity Example 2: Simplify (x² - 6x + 9 ) ÷ (x – 3) Step1:- Write the question in fraction form Step2:- Factorise Polynomial by taking common factors Compare with suitable Identity x2+ (a + b)x + ab = (x + a) (x + b) x² - 6x + 9 We need to find value of a and b such that a + b = -6, ab = 9 a b a + b ab a+b=-6 ab=9 choice 1 9 10 9 no yes ∴ a=-3 and b=-3 3 3 6 9 no yes -3 -3 -6 9 yes yes

Substitute a=-3 and b=-3 in the above equation = (x + (-3)) (x + (-3)) Continue Substitute a=-3 and b=-3 in the above equation = (x + (-3)) (x + (-3)) =(x - 3) (x – 3) Step3:- Cancel out common factors in both the numerator and denominator Cancelling (x-3) in both numerator and denominator = x - 3

Try these 1) (6z3 + 15z2) ÷ (3z4 + 6z2) 2) (m2 − 7m + 10) ÷ (m − 5)