SOLUTION: Use synthetic division to find the quotient and the remainder of {{{(2x^4-x^3-15x^2+3x)/(x+3)}}}

Question 882932: Use synthetic division to find the quotient and the remainder of

Answer by cigany29(23) (Show Source): You can put this solution on YOUR website!

to find the test zero we say so so our test zero is -3.
Set up our synthetic division table by using all the coefficients from the equation. Remember, there is no constant in you r equation so you replace it with 0 in your division table:
.........2..........-1..........-15..........3..........0
-3|

bring down your first term (2) and multiply it by your test zero of -3 to get -6. You are going to add this number to the next coefficient in the table to get -7:
.........2..........-1..........-15..........3..........0
-3|..................+
......................-6
..........2..........-7
continue multiplying each answer with your test zero and adding it to the term in the next column:
........2...........-1............-15..........3...........0
........................+..............+...........+...........+
-3|................-6.............21.........-18 .......45

........2...........-7..............6...........-15........|45
so your remainder is 45.
To find your quotient, use the coefficients produced at the bottom of every column in your table (except the remainder column- we'll get to that last) and in descending order of exponents beginning with one less than the highest exponent in your original equation pair with your coefficients at the bottom of the column to get:

the last coefficient or your remainder is placed over your original divisor to indicate it is the remainder.
Putting it all together we get:=
And in remainder form it looks like this: = remainder 45.
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