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Sagot :
Answer:
(x + 7 ) ( x - 12 )
Explanation:
We know that if we multiply any two expressions x + a and x + b then we have
[tex](x+a)(x+b)=x^2+(a+b)x+ab[/tex]Now similarly,
[tex]x^2+(a+b)x+ab=x^2-5x-84[/tex]meaning
[tex]\begin{gathered} a+b=-5 \\ ab=-84 \end{gathered}[/tex]In other words, what are the two numbers that if I add them together I get -5 and If I multiply them I get -84. The answer comes from educated guesses. We guess that if we add 7 and -12 we get 5 and if we multiply then we get -84; therefore,
[tex]\begin{gathered} a=7 \\ b=-12 \end{gathered}[/tex]Hence, the expression can be factored as
[tex]=x^2-5x-84=(x-12)(x+7)[/tex]which is our answer!
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