PDF chapter test TRY NOW
Learn to factorize the expression of the form .
Procedure to factorize the expression.
Step 1: Determine the coefficient \(a, b\) and \(c\).
Step 2: Calculate the product of \(a\) and \(c\). Product \(= ac\) and sum \(= b\). Thus the middle coefficient is the sum and extreme product is the product value.
Step 3: Express the middle term as sum of two terms such that the sum satisfies the middle term and the product satisfies the extreme product.
Step 4: Now group the expression into two factors by taking the common expression outside.
Example:
1. \(x^2+5x+6\)
We have \(a =1\), \(b = 5\) and \(c = 6\).
Here the product \(=\) \(a \times c\) \(=\) \((1 \times 6)\) \(= 6\) and sum \(= b = 5\).
We need to choose two number such that the sum of two numbers is \(5\) and the product of two numbers is \(6\).
\((2+3) = 5\) and \((2 \times 3\) \(= 6\)
We can write as follows.
\(x^2+5x+6\) \(=\) \(x^2+3x+2x+6\)
\(=\)\(x(x+3)+2(x+3)\)
\(=\) \((x+3)(x+2)\)
2. \(2x^2-5x-3\)
We have \(a = 2\), \(b = -5\) and \(c = -3\).
Here the product \(=\) \(a \times c\) \(=\) \((2 \times -3)\) \(=\) \(-6\) and sum \(= b = -5\).
We need to choose two number such that the sum of two numbers is \(-5\) and the product of two numbers is \(-6\).
\((-6+1) = -5\) and \((-6\times 1)\)) \(=-6\)
We can rewrite as follows.
\(2x^2-5x-3\) \(=\) \(2x^2-6x+x-3\)
\(= 2x(x-3)+1(x-3)\)
\(= (x-3)(2x+1)\)
Register for free to see more content