Question 161384: CAN SOMEONE PLEASE HELP ME WITH THIS PROBLEM:
Use synthetic division to show that the number given to the right of the equation is a solution of the equation, then solve the polynomial equation.
x^3 + 2x^2 - 11x - 12 = 0;-4
Answer by ilana(307)   (Show Source):
You can put this solution on YOUR website! Synthetic division is fun!!!
Start by writing the "solution" in the top left corner, in a small box. To the right of the box, write the coefficients of the polynomial.
So you have:
____-4____1__2__-11__-12
Now draw an arrow coming down from the "1" and draw a horizontal line below that arrow. Write a "1" directly below the arrow. So you have a arrow pointing from a "1" to another "1". Now multiply that bottom "1" by the number in the box, "-4". So you get "-4". So write "-4" directly below the next number to the right, "2". So the second row has an arrow and then a "2". Now add the "2" at the top of the column to the number right below it, "-4", to get "-2". Write "-2" at the bottom of that column. Now multiply that "-2" by the number in the box, "-4", to get "8". So write "8" in the next column in the second row. Then add the numbers in that column. Then multiply that answer by the number in the box again. Continue the pattern until you have filled in all the spaces below the coefficient. That is called synthetic division. This shows that -4 is a solution to the equation because the last number in the last row is 0, which really means that (x^3 + 2x^2 - 11x - 12) divided by (x + 4) has a remainder of 0, or (x + 4) is a factor of (x^3 + 2x^2 - 11x - 12), or -4 is a solution of the equation x^3 + 2x^2 - 11x - 12 = 0.
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