Discover answers to your most pressing questions at Westonci.ca, the ultimate Q&A platform that connects you with expert solutions. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

What would be the correct way to solve this?[tex] {x}^{2} - 5x - 84[/tex]

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!

We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.