How do you show that x+7 is a factor of #x^3-37x+84#. Then factor completely?

1 Answer
Aviv S.
Mar 18, 2018

The completely factored form is #(x+7)(x-3)(x-4)#.

Explanation:

You can use synthetic division. I'm not going to explain how to do synthetic division here, but this website has a really good explanation of how it works.

![https://www.mathportal.org/calculators/polynomials-solvers/http://synthetic-division-calculator.php](https://useruploads.socratic.org/KTlencyITI6Rf3czisQI_Screen%20Shot%202018-03-17%20at%207.00.28+PM.png)

Now we have our polynomial as #(x+7)(x^2-7x+12)#.

We can factor our quadratic using #-3# and #-4#:

#color(white)=(x+7)(x^2-7x+12)#

#=(x+7)(x^2-3x-4x+12)#

#=(x+7)((x-3)(x-4))#

#=(x+7)(x-3)(x-4)#

This is the fully factored polynomial. Hope this helped!

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