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Home >> Polynomials >> Factoring of Quadratic Polynomials >> Factoring of Quadratic Polynomials
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} = a^{2} + 2ab + b^{2} 2) (a  b)^{2} = a^{2}  2ab + b^{2} 3) a^{2}  b^{2} = (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 : 4z^{2} + 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} = a^{2} + 2ab + b^{2} and we get
Squaring first term 4z^{2} = (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 : 4z^{2}  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} = a^{2}  2ab + b^{2} and we get
Squaring first term 4z^{2} = (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 : 4z^{2}  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 a^{2}  b^{2} = (a + b) (a  b) and we get
Squaring 4z^{2} = (2z)^{2} Squaring term 9 = (3)^{2}
a^{2}  b^{2} = (2z)^{2}  (3)^{2} a^{2}  b^{2} = (2z  3) (2z + 3)
Study More Solved Questions / Examples
Factorize the following 
A) 9y^{2} + 24y + 16
B) 9x^{2}  16
C) 4y^{2}  12y + 9
D) 144x^{2} + 24x + 1
E) 36y^{2}  60y + 25
F) 16x^{2}  64
G) x^{3}  x
H) 4x^{2}  (2y  z)^{2} 
 
