divide the polynomial x3-9x2+23x-18 by x2-4x+3and find the quotient and the remainder
Answers
Answer:
Set up a table with the coefficients of the dividend on the first row (
row A
below) leaving a little extra space at the beginning of the line.
Leave a blank line (to be filled in as we go along).
Write the negative of the divisor at the far left of the third line (
row C
below).
You should have something that looks like:
XXXX
x
3
XX
x
2
XX
x
1
XX
x
0
XXx
∣
XX
1
XX
9
XX
23
XX
15
X
row A
xxx
∣
XXXXXXXXXXXX
−−−−−−−−−−−−−−−−−−−−−−−
row B
−
5
x
∣
XXXXXXXXXXXXXX
row C
For each coefficient column in turn from left to right:
Add the value in
row B
to the (coefficient) value in
row A
and write the result in
row C
Multiply the negative divisor (on the far left of
row C
) by the value just written in
row C
and writer the product in the next column of
row B
After processing the first column, your result should look like:
XXx
∣
XX
1
XX
9
XX
23
XX
15
X
row A
XXx
∣
XXxx
−
5
XXXXXXX
−−−−−−−−−−−−−−−−−−−−−−−−
row B
−
5
x
∣
X
1
XXXXXXXXXXXx
row C
...and after processing all the columns, like:
XXx
∣
XX
1
XX
9
XX
23
XX
15
X
row A
XXx
∣
XXxx
−
5
x
−
20
x
−
15
−−−−−−−−−−−−−−−−−−−−−−−−−
row B
−
5
x
∣
X
1
XX
4
XXX
3
XX
0
X
row C
The final result in
row C
gives the coefficients of the resulting quotient plus (as the last value in
row C
the remainder:
−
5
x
∣
X
1
XX
4
XXX
3
−−−−−−−−−−−
XX
0
XXXXXXX
row C
XXXX
x
2
XX
x
1
XX
x
0
XX
Remainder