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.

Algebra ->  Percentage-and-ratio-word-problems -> 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.      Log On


   

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) About Me  (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

%28-x%5E2%2B2x-5%29%283x%2B2%29
%28-x%5E2%2B2x-5%29%283x%29%2B%28-x%5E2%2B2x-5%29%282%29

%28-3x%5E3%29%2B%286x%5E2%29%2B%28-15x%29%2B%28-2x%5E2%29%2B%284x%29%2B%28-10%29

(2) combine like terms

%28-3x%5E3%29%2B%286x%5E2-2x%5E2%29%2B%28-15x%2B4x%29%2B%28-10%29
-3x%5E3%2B4x%5E2-11x-10

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) About Me  (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) About Me  (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