How do we middle term split in maths
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How do we middle term split in maths

[From: ] [author: ] [Date: 11-05-31] [Hit: ]
you will get 4 terms. combine first two and last two. take common.if b is negative a can be splited into two no such that subtraction of those nos is equal to a.then all sameeg: X^2+3X+2=0X^2+(2+1)x+2=0(X^2+2x)+(x+2)=0x(x+2)+1(x+2)=0(x+1)(X+2)=0again,3X^2+X-4=03X^2+(4-3)x-4=03X^2+4x-3x-4=0x(3x+4)-(3x+4)=0(x-1)(3x+4)=0if co-eff of x^2 is other than 1 ,......
co-eff of X^2 must be positive to understand easily.
if bis positive, 'a' can be splited into two no such that sum of those nos is equal to a. keep the sign of a as it is. separate the terms. you will get 4 terms. combine first two and last two. take common.
if b is negative 'a' can be splited into two no such that subtraction of those nos is equal to a.then all same

eg: X^2+3X+2=0
X^2+(2+1)x+2=0
(X^2+2x)+(x+2)=0
x(x+2)+1(x+2)=0
(x+1)(X+2)=0

again,3X^2+X-4=0
3X^2+(4-3)x-4=0
3X^2+4x-3x-4=0
x(3x+4)-(3x+4)=0
(x-1)(3x+4)=0


if co-eff of x^2 is other than 1 , then the sum or subtraction of two no will be the product of co-eff of X^2 and b(see the last eg) all steps including sign convention will be same.

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x^2 + 5x+6
ab=6 and a+b=5
solve these two by hit and trial
and get a= 3 and b=2
so, x^2 + 2x +3x +6= x(x+2) + 3(x+2)= (x+3)(x+2)

x^2 -5x +6
ab=6 and a+b= -5
a= -3 and b=-2
x^2 -3x-2x + 6 = x(x-3) -2(x-3)=(x-2)(x-3)
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