Factoring of Quadratic Polynomials

Factoring Quadratic Polynomials by Splitting Middle Term

Before you understand how to factorize quadratic polynomials, you should read What are Polynomials ? What are Quadratic Polynomials ? There are 3 formulas to factor a quadratic polynomial 1) (a + b)2 = a2 + 2ab + b2 2) (a - b)2 = a2 - 2ab + b2 3) a2 - b2 = (a + b) (a - b) To factorize a given polynomial using the above formulas we will first check that whether we can square the first and last term, if we cannot then instead of these formulas we will use Splitting the Middle Term formula for factorization Let's first study some examples on these 3 formulas Example : 4z2 + 12z + 9 Solution : As we can square the first and last term, and all arithmetic signs are of addition we will use the formula (a + b)2 = a2 + 2ab + b2 and we get Squaring first term 4z2 = (2z)2 Squaring last term 9 = (3)2 (a + b)2 = (2z)2 + 2 X 2z X 3 + (3)2 (a + b)2 = (2z + 3)2 Example : 4z2 - 12z + 9 Solution : As we can square the first and last term, and arithmetic sign of middle term is of subtraction we will use the formula (a - b)2 = a2 - 2ab + b2 and we get Squaring first term 4z2 = (2z)2 Squaring last term 9 = (3)2 (a - b)2 = (2z)2 - 2 X 2z X 3 + (3)2 (a - b)2 = (2z - 3)2 Example : 4z2 - 9 Solution : As this polynomial has 2 terms and we can square the first and last term and arithmetic sign is of subtraction we will use the formula a2 - b2 = (a + b) (a - b) and we get Squaring 4z2 = (2z)2 Squaring term 9 = (3)2 a2 - b2 = (2z)2 - (3)2 a2 - b2 = (2z - 3) (2z + 3) Study More Solved Questions / Examples Factorize the following - A) 9y2 + 24y + 16 B) 9x2 - 16 C) 4y2 - 12y + 9 D) 144x2 + 24x + 1 E) 36y2 - 60y + 25 F) 16x2 - 64 G) x3 - x H) 4x2 - (2y - z)2