Partial Fractions (P3)Watch

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Thread starter 14 years ago
#1
I still hate this topic. How do I go about doing this Q?

1.)
a.) Find the quotient & remainder obtained in dividing (x³+4x²-2) by (x²+x-2).

b.) Hence, express (x³+4x²-2)/(x²+x-2). in partial fractions.
0
14 years ago
#2
a.) Find the quotient & remainder obtained in dividing (x³+4x²-2) by (x²+x-2).

(x²+x-2) clearly factorises to (x-1)(x+2)

(x³+4x²-2)/(x²+x-2) = (x³+4x²-2)/(x-1)(x+2) = [(x³+4x²-2)/(x-1)].[1/(x+2)] = [(x³+4x²-2)/(x-1)]/(x+2)

first use long division to evaluate [(x³+4x²-2)/(x-1)] = (x²+5x+5) + 3/(x-1) so:

(x³+4x²-2)/(x²+x-2) = [(x²+5x+5) + 3/(x-1)]/(x+2) = (x²+5x+5)/(x+2) + [3/(x-1)]/(x+2) = (x²+5x+5)/(x+2) + [(x-1)/3](x+2)

by long division again we know (x²+5x+5)/(x+2) = x + 3 - 1/(x+2) so:

(x²+5x+5)/(x+2) + [(x-1)/3](x+2) = x + 3 - 1/(x+2) + (x-1)(x+2)/3

lalala.. better than this method, teach yourself to do algebreis division when the quotient is a quadratic.
0
14 years ago
#3
(Original post by Slice'N'Dice)
I still hate this topic. How do I go about doing this Q?

1.)
a.) Find the quotient & remainder obtained in dividing (x³+4x²-2) by (x²+x-2).

b.) Hence, express (x³+4x²-2)/(x²+x-2). in partial fractions.
Please look at attachment ...
0
14 years ago
#4
(Original post by Galois)
Please look at attachment ...
Wow! Did you use LaTex? 0
Thread starter 14 years ago
#5
Many thanks guys. 0
14 years ago
#6
(Original post by Slice'N'Dice)
I still hate this topic. How do I go about doing this Q?

1.)
a.) Find the quotient & remainder obtained in dividing (x³+4x²-2) by (x²+x-2).

b.) Hence, express (x³+4x²-2)/(x²+x-2). in partial fractions.
im bored. here's an alternative approach
f(x)=(x^3+4x^2-2)
g(x)=x^2+x-2
want to write f(x)=q(x)g(x)+r(x)
clear that q(x) and r(x) linear terms
so want to find a,b,c,d st.
f(x)=(ax+b)g(x)+(cx+d)
since g(x)=(x+2)(x-1)
f(1)=3=c+d
f(-2)=6=-2c+d so c=-1 and d=4
then f(x)=(ax+b)g(x)+4-x
f(0)=-2=-2b+4 so b=3
f(2)=22=(2a+3)(4)+2
so a=1
hence
f(x)=(x+3)g(x)+(4-x)
ii) f(x)/g(x)=x+3+(4-x)/(x+2)(x-1)
(4-x)/(x+2)(x-1)=A/(x+2)+B/(x-1)
by the cover up method
A=4-x/x-1 when x=-2 ie A=-2
B=4-x/(x+2) when x=1 ie B=1
so f(x)/g(x)=x+3+1/(x-1)-2/(x+2).
0
14 years ago
#7
(Original post by J.F.N)
Wow! Did you use LaTex? Well MathType was taking too long so I resolved to good old Paint 0
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