How to factor x^2−10x−24?

BySolutionlogy
How to factor x^2−10x−24?Question: How to factor x2−10x−24? 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+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 x2−10x−24 as (x2−12x)+(2x−24). (x2−12x)+(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 x2−10x−24 are (x−12)(x+2) Conclusion On factorizing x2−10x−24 we get (x−12)(x+2)

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