1. Find synthetic division of x2-10x+25 and x-5Solution:x2-10x+25x-5 using synthetic division
To determine root divisor, we have to solve divisor equation
x-5=0:. our root becomes
x=5Write coefficients of the dividend
x^2-10x+25 to the right and our root
5 to the left
Step-1 : Write down the first coefficient
1Step-2 : Multiply our root
5 by our last result
1 to get
5 [
5 ×
1=
5 ]
Step-3 : Add new result
5 to the next coefficient of the dividend
-10, and write down the sum
-5, [
(-10) +
5=
-5 ]
Step-4 : Multiply our root
5 by our last result
-5 to get
-25 [
5 ×
(-5)=
-25 ]
Step-5 : Add new result
-25 to the next coefficient of the dividend
25, and write down the sum
0, [
25 +
(-25)=
0 ]
We have completed the table and have obtained the following coefficients
1,-5,0All coefficients, except last one, are coefficients of quotient, last coefficient is remainder.
Thus quotient is
x-5 and remainder is
0