What is the sum of the quotient and remainder, by the following division algorithm. 32679÷265.
Answers
Answer:
The answer is b123.31698113207 reciprocal link it you can do it long division method and some other ways.
this is your answer
Answer:
Explanation:
Step-1
We start by figuring out the first multiplier:
x
2
×
(
?
)
=
x
4
Clearly, this multiplier will be
x
2
. We multiply this multiplier with the divisor, and carry out subtraction as follows:
x
2
+
x
+
2
x
2
⎞
⎟
⎠
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
x
4
−
3
x
3
+
2
x
2
−
7
x
+
4
x
4
+
x
3
+
2
x
2
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
−
4
x
3
+
0
x
2
−
7
x
The expression at the bottom is our new dividend.
Step-2
Now, we have to figure out our next multiplier:
x
2
×
(
?
)
=
−
4
x
3
Thus, we have:
x
2
+
x
+
2
x
2
−
4
x
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎠
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
x
4
−
3
x
3
+
2
x
2
−
7
x
+
4
x
4
+
x
3
+
2
x
2
–––––––––––––––––––––––
−
4
x
3
+
0
x
2
−
7
x
−
4
x
3
−
4
x
2
−
8
x
––––––––––––––––––––––
4
x
2
+
x
+
4
Step-3
The next multiplier is similarly obtained:
x
2
×
(
?
)
=
4
x
2
Thus,
x
2
+
x
+
2
x
2
−
4
x
+
4
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎠
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
x
4
−
3
x
3
+
2
x
2
−
7
x
+
4
x
4
+
x
3
+
2
x
2
–––––––––––––––––––––––
−
4
x
3
+
0
x
2
−
7
x
−
4
x
3
−
4
x
2
−
8
x
––––––––––––––––––––––
4
x
2
+
x
+
4
4
x
2
+
4
x
+
8
––––––––––––––––
−
3
x
−
4
The degree of the last expression is less than that of the divisor, which means that the division process has to stop now. Thus, the quotient and the remainder polynomials are (respectively):
q
(
x
)
:
x
2
−
4
x
+
4
r
(
x
)
:
−
3
x
−
4