Divide using synthetic division (x^2+15x+52) by x+9
To divide using synthetic division, we will use the coefficients of the polynomial and the divisor.
The given polynomial is x^2 + 15x + 52, and the divisor is x + 9.
First, write down the coefficients of the polynomial (including any zero placeholders):
1 15 52
Now, write the divisor in the synthetic division format, changing the sign to -9 (since we are dividing by x + 9):
-9
To start the synthetic division process, bring down the first coefficient (1) to the line below:
1
Next, multiply the divisor (-9) by the number at the bottom (1) and write the result under the second coefficient:
1 -9
Then, add the result to the second coefficient (15):
1 -9
+ 15
____________
Finally, repeat the process by multiplying the result (6) by the divisor (-9) and writing the result under the third coefficient (52):
1 -9 6
+ 15
____________
1 -9 6
The final line of coefficients represents the quotient, and the last number (6) is the remainder.
Therefore, the division of x^2 + 15x + 52 by x + 9 is:
Quotient: x - 9
Remainder: 6