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# How to factor x^2−10x−24?

How to factor x^2−10x−24? a Question : How to factor x 2 − 10x − 24 ? a Solution : We have to find the factors of given quadratic equation Factoring out the expression by grouping . First , the expression needs to be rewritten as x 2 + ax + bx − 24. To find a and b , we will set up a system to be solved . a + b = − 10 ab = 1 ( − 24 ) = − 24 Since ab is negative , a and b have the opposite signs . Since a + b is negative , the negative number has greater absolute value than the positive . Listing all such integer pairs that give product 1 , − 24 2 , − 12 3 , − 8 4 , − 6 Calculating the sum for each pair , we get 1 − 24 = − 23 2 − 12 = − 10 3 − 8 = − 5 4 − 6 = − 2 The solution is the pair that gives sum − 10. a = − 12 b = 2 Rewriting x 2 − 10x − 24 as ( x 2 − 12x ) + ( 2x − 24 ) . ( x 2 − 12x ) + ( 2x − 24 ) Factoring out x in the first and 2 in the second group , we get x ( x − 12 ) + 2 ( x − 12 ) Factor out common term x − 12 by using distributive property . ( x − 12 ) ( x + 2 ) Hence , the factors of x 2 − 10x − 24 are ( x − 12 ) ( x + 2 ) Conclusion On factorizing x 2 − 10x − 24 we get ( x − 12 ) ( x + 2 )
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