Welcome to Westonci.ca, the place where your questions are answered by a community of knowledgeable contributors. Discover the answers you need from a community of experts ready to help you with their knowledge and experience in various fields. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

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!

Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.