Divide 6 + x − 4x ^2+ x ^2by (x − 3) by long division method.
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Answers
Answer:
It is better to rearrange the divisor in the same descending form as the dividend.
-1/2x2+11/4x + 3/8
-2x + 1 )x3 - 6 x2 + 2x + 4
x3 - 1/2 x2 (1)
-11/2 x2 + 2 x
-11/2 x2 +11/4x (2)
-3/4 x + 4
-3/4 x +3/8 (3)
R 29/8
Explanation:
(1) We divide (x3) by (-2x). The answer is (-1/2x2). This is the first term of the polynomial answer.
Next, we multiply (-1/2x2) and (-2x +1). The answer is (x3-1/2x2).
As in numeric long division, we subtract:
x3 - 6x2
-
x3 - 1/2x2
The result of subtraction is (-11/2 x2)
(2) We bring down (+2x) and repeat the process from (1).
We divide (-11/2x2) by (-2x). The answer is (11/4 x). This is the next term in the polynomial answer.
We multiply (11/4 x) by the divisor (-2x + 1) and subtract (I will do this on one line).
-11/2 x2 +2x - (-11/2 x2+11/4x) = 2x - 11/4x = -3/4x.
(3) We bring down (+4) and repeat the process from (1) again.
We divide (-3/4x) by (-2x). The answer is (+3/8).
We multiply (+3/8) by the divisor (-2x+1) and subtract (I will do this on one line).
-3/4x +4 -(-3/4x +3/8) = 4 - 3/8 = 29/8.
This is where we stop. The remainder is 29/8.
For comparison, check the long division below:
165
3)496
3
19
18
16
15
R1