Division of a Polynomial by a Monomial Division

Division of a Polynomial by a Monomial

Division of a Polynomial by Monomial While dividing polynomials by monomial, do the following steps Step 1: - Write the question in fraction form Step 2: - Divide each term in the numerator by the term in the denominator Step 3: - Simplify each term and use the rules for exponents to simplify the variables in each term and reduce the fractions. Remember your exponent laws for dividing. You subtract the exponents if the base is the same. For example: am = am - n an a 5 = a 5 -3 = a 2 a 3

Example 1: Simplify, (5 x 2 – 10 x) ÷ 5 Step 1: - Write the question in fraction form = 5 x 2 – 10 x 5 Step 2: - Divide each term in the numerator by the term in the denominator = 5 x 2 5 10 x 5 - Step 3: - Simplify each term and use the rules for exponents to simplify the variables in each term and reduce the fractions. 5 x 2 5 - 2 10 x 5 = x 2 – 2 x

Example 2: Simplify, (3 b 3 – 6 b 2 + 9 b) ÷ 6 b Step 1: - Write the question in fraction form = 3 b 3 – 6 b 2 + 9 b 6 b Step 2: - Divide each term in the numerator by the term in the denominator = 3 b 3 6 b - 6 b 2 6 b + 9 b 6 b Step 3: - Simplify each term and use the rules for exponents to simplify the variables in each term and reduce the fractions. b 3 ÷b 1 = b 2 ÷b 1 =b 1= b 3 - 6 b 2 2 6 b 6 b + 9 b 6 b 2 3 = b 2 - b + 3 2 2

Division of a Polynomial by Monomial Common factor Method While dividing polynomials by monomial, do the following steps Step 1: - Write the question in fraction form Step 2: - Factorise Polynomial by taking common factors Step 3: - Simplify constants in both numerator and denominator and use the rules for exponents to simplify the variables and reduce the fractions. Remember your exponent laws for dividing. You subtract the exponents if the base is the same. For example: am = am - n an a 5 = a 5 -3 = a 2 a 3

Example 1: Simplify (5 x 2 – 10 x) ÷ 5 Step 1: - Write the question in fraction form = 5 x 2 – 10 x 5 Step 2: - Factorise Polynomial by taking common factors = 5(x 2 – 2 x) 5 Step 3: - Simplify constants in both numerator and denominator and use the rules for exponents to simplify the variables and reduce the fractions. = = 5(x 2 – 2 x) 5 x 2 – 2 x

Example 2: Simplify (3 b 3 – 6 b 2 + 9 b) ÷ 6 b Step 1: - Write the question in fraction form 3 2 = 3 b – 6 b + 9 b 6 b Step 2: - Factorise Polynomial by taking common factors 2 = 3 b(b – 2 b + 3) 6 b Step 3: - Simplify constants in both numerator and denominator and use the rules for exponents to simplify the variables and reduce the fractions. = = = 3 b(b 2 – 2 b + 3) 2 6 b b 2 – 2 b + 3 2 2 2 = b 2 – b + 3 2 2 Divide each term in the numerator by the term in the denominator Simplify each term and use the rules for exponents to simplify the variables in each term and reduce the fractions.

Try these 1) 9 x 2 – 6 x 3 2) 12 b 3 – 18 b 2 + 36 b 6 b