SOLUTION: Find the product of -x^2 + 2x - 5 and 3x + 2 _x^3 + _x^2 + _x + _ Use the given numbers to fill in the blanks 3. -3. 4. -4. 10. -10. 11. -11.

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Question 1205248: Find the product of -x^2 + 2x - 5 and 3x + 2
_x^3 + _x^2 + _x + _
Use the given numbers to fill in the blanks
3.
-3.
4.
-4.
10.
-10.
11.
-11.
Found 3 solutions by greenestamps, mccravyedwin, math_tutor2020:
Answer by greenestamps(13209)   (Show Source): You can put this solution on YOUR website!


This is a straightforward process....

(1) multiply each term of one polynomial by each term of the other






(2) combine like terms




If that work is hard to follow, you might find this easier to understand....

          -x^2  +  2x  +  -5
        *          3x  +   2
         --------------------
         -2x^2  +  4x  + -10
  -3x^3  +6x^2  + -15x
 ----------------------------
  -3x^3 + 4x^2  + -11x + -10
Answer by mccravyedwin(408)   (Show Source): You can put this solution on YOUR website!
       -x2 +  2x -  5  
              3x +  2
      -2x2 +  4x - 10
-3x3 + 6x2 - 15x     
-3x3 + 4x2 - 11x - 10

Edwin
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

I'll use the box method

-x^2+2x-5 has 3 terms
3x+2 has 2 terms
We'll have a table that has 3 rows and 2 columns.
Place the terms as headers along the top and left side like so
3x   2    
-x^2
2x
-5


To fill out this table, multiply the headers.
Example: -x^2 times 3x = -3x^3 in the upper left corner.
3x2
-x^2-3x^3-2x^2
2x6x^24x
-5-15x-10

Add up the results. Combine like terms.
-3x^3 + (-2x^2) + 6x^2 + 4x + (-15x) + (-10)
-3x^3 -2x^2 + 6x^2 + 4x - 15x - 10
-3x^3 +(-2x^2 + 6x^2) + (4x - 15x) - 10
-3x^3 + 4x^2 - 11x - 10

Therefore,
(-x^2+2x-5)(3x+2) = -3x^3 + 4x^2 - 11x - 10

------------------------------------------------------------------

Let's look at another approach.
This time I'll use the distributive property.

Let y = 3x+2

(-x^2+2x-5)(3x+2)
= (-x^2+2x-5)y
= y(-x^2+2x-5)
= -x^2*y + 2xy - 5y
= -x^2(3x+2) + 2x(3x+2) - 5(3x+2)
= -3x^3 - 2x^2 + 6x^2 + 4x - 15x - 10
= -3x^3 + 4x^2 - 11x - 10

Note on the 2nd to last line, all of the terms mentioned are found inside the 6 inner boxes of the previous method.

------------------------------------------------------------------

Or we could have these steps.

Let w = -x^2 + 2x - 5

(-x^2+2x-5)(3x+2)
= w(3x + 2)
= 3xw + 2w
= 3x(-x^2 + 2x - 5) + 2(-x^2 + 2x - 5)
= -3x^3 + 6x^2 - 15x - 2x^2 + 4x - 10
= -3x^3 + 4x^2 - 11x - 10
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