1. Division of a Polynomial by a Binomial

2. 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:

3. 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

4. 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

5. 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

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