ng steps: -et us look at what we have done in the process above as a whole:
+
rom the dividend - 2x - 1. This gives us 1
y - 2 and subtract the product
2x - 2
+1
think that xi
s the remainder.
This process continues till the remainder is 0 or the degree of the new dividend is less
nomial by ghan the degree of the divisor. At this stage, this new dividend becomes the remainder
ind the sum of the quotients gives us the whole quotient.
štep 6 : Thus, the quotient in full is 3x – 2 and the remainder is 1.
1 + x
andard fon
3x - 2
So, the
x+1)
1) 3x2 + x - 1
3x² + 3x
- 2x - 1
quotient
- 2x-2
1
Notice that 3x2 + x-1 = (x + 1) (3x - 2) + 1
i.e. Dividend = (Divisor x Quotient) + Remainder
In general, if p(x) and g(x) are two polynomials such that degree of p(x) degree of
g(x) and g(x) +0, then we can find polynomials q(x) and r(x) such that:
p(x) = g(x)q(x) + r(x),
where r(x) = 0 or degree of r(x) < degree of g(x). Here we say that p(x) divided by
or giver
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