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Find the constant coefficient when the polynomial 3(x - 4) + 2(x^2 - x + 7) - 5(x - 1) is simplified.

 Mar 21, 2020
 #1
avatar+483 
+1

Hey qwerty, glad to see you again!

 

This problem is just some expanding and then rearranging. 

Let's start with an understanding of the word "constant". the constant of any polynomial is defined as the term that has an x coefficient of "0"; in other words, it has no "x" coefficient. 

Now that we know this, it's a simple matter of distributing and multiplying out everything and then combining like terms. We get:

\(3(x - 4) + 2(x^2 - x + 7) - 5(x - 1) = 3x-12 + 2x^2-2x+14-5x+5\)

Combining like terms, we get:

\(2x^2-4x+7\)

Because the problem asks for the constant coefficient, we then get:

 

as our final answer

 Mar 21, 2020
 #2
avatar+23566 
+1

Good answer , jfan....

    you could judt multiply out the constant factors  (all of the rest will have some 'x' in them)

      3(-4)  + 2(7) -5(-1)    =  7

 Mar 21, 2020
 #3
avatar+1956 
+1

We can expand \(3(x - 4) + 2(x^2 - x + 7) - 5(x - 1)\)  to find the constant coefficient.

 

This will get us \(3x-12+2x^2-2x+14-5x+5.\)

 

Adding and subtracting "like" terms, this will get us \(2x^2-4x+7.\)

 

This will get us 7 as the constant coefficient, like jfan17 said.

 

Hope this helped!laugh

 Mar 21, 2020
 #4
avatar+111321 
0

Thanks, jfan  and CTG !!!!!

 

 

cool cool cool

CPhill  Mar 21, 2020

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