Question - Factoring Quadratic Expression
mathsolving quadratic equationsfactoring polynomialsfactoring quadratic expressionquadratic equation factors
Solution:
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 $$ (3x - 2y)(2x + 7y) $$.
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