Discover the answers to your questions at Westonci.ca, where experts share their knowledge and insights with you. Discover a wealth of knowledge from experts across different disciplines on our comprehensive Q&A platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

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. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.