How to factor x^2−10x−24?

How to factor x^2−10x−24?Question: How to factor x210x24? 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 x2+ax+bx24. 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 124=23 212=10 38=5 46=2 The solution is the pair that gives sum 10. a=12 b=2 Rewriting x210x24 as (x212x)+(2x24). (x212x)+(2x24) Factoring out x in the first and 2 in the second group, we get x(x12)+2(x12) Factor out common term x12 by using distributive property. (x12)(x+2) Hence, the factors of x210x24 are (x12)(x+2) Conclusion On factorizing x210x24 we get (x12)(x+2)

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