Example Question - factoring quadratic expression

Factoring Quadratic Expression

To solve the given expression which is \( 6x^2 + 17xy - 14y^2 \), we look for two numbers which when multiplied give the product of \( 6x^2 \) and \( -14y^2 \) (which is \( -84x^2y^2 \)) and when added give the middle term \( 17xy \). These two numbers are 21 and -4. Now, we can rewrite the middle term \( 17xy \) as \( 21xy - 4xy \). The expression becomes: \[ 6x^2 + 21xy - 4xy - 14y^2 \] Next, we group the terms to factor by grouping: \[ (6x^2 + 21xy) - (4xy + 14y^2) \] Factor out the common factor from each group: \[ 3x(2x + 7y) - 2y(2x + 7y) \] Now we can see that \( (2x + 7y) \) is a common factor: \[ (3x - 2y)(2x + 7y) \] So the factored form of \( 6x^2 + 17xy - 14y^2 \) is \( (3x - 2y)(2x + 7y) \).