Find q, r in \mathbb{Z} so that 105 = 11q + r
1 answer:
Answer:
Step-by-step explanation:
Division Algorithm :
As per division algorithm , for numbers a and b , there exist numbers q and r such that
Here ,
a = Dividend
b = Divisor
q = quotient
r = remainder
Given : 105 = 11q + r such that
Here, clearly a = 105 , b = 11
To find : q and r
Solution : On dividing 105 by 11 , we get
On comparing with
, we get
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Answer:
Input value: 3
Step-by-step explanation:
If I'm understanding the question correctly it would look like this.
Next: Subtract one
Divide by three to get x.
Answer:
Step-by-step explanation:
In the first part the given polynomial is , we have to divide this polynomial by (x-1) using synthetic division.
Here are the steps of synthetic division
Step 1: Set up the synthetic division table in which the coefficients are written in descending power of x.
Step 2: Drop down the leading coefficient i.e the coefficient of highest power of x to the bottom row.
Step 3: Multiply a by the value just written on the bottom row and write this value just down of the number written next of leading coefficient. Here, a is 1(taken from divisor)
Step 4: Add the column made in step 3. Repeat these steps until the last column reached.
In the second part,
It is given that divisor polynomial is the factor of given polynomial then we have to tell the remainder which is 0 because if divisor polynomial is the factor the it will completely divide the given polynomial which gives remainder 0.
In the third part,
Given when one uses the synthetic division to divide by (x-3) then what number is used to multiply each term that is dropped down or added.
As explained the steps of synthetic division in first part
x-3=0 ⇒ x=3 which is a
In step 3, Multiply a by the value just written on the bottom row and write this value just down of the number written next of leading coefficient. So, 3 is multiplied.
As explained in Step 2: Drop down the leading coefficient i.e the coefficient of highest power of x to the bottom row.
The columns which is formed by above steps are added.
