ELEMENTARY ALGEBRA SHORTCUTS FOR QUANTITATIVE APTITUDE
Algebraic Expressions: .a number , including literal numbers , along with the signs of fundamental operations .
Eg: Find the sum of
1) -15a2 +3ab -6b2 , a2 -5ab + 11b2 ,-7a2 -18ab -13b2 and 26a2
-16ab -7b2
Ans- 5a2 -36ab -15b2
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Remainder Theorem: this theorem represents the relationship between the divisor of the first degree in the form (x-a) and the remainder r(x)
Q: Find the remainder when 27x3 -9x2 +3x- is divided by 3x+2
Ans : 3x+2=0 , x = -2/3
remainder is f(-2/3)
f(-2/3) = 27(-2/3)3 -9(-2/3)2 +3(-2/3) -8
= -8-4-2-8 = -22
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CONDITIONS OF DIVISIBILITY:
1) xn + an is exactly divisible by (x + a) only when n is odd.
2) xn +an is never divisible by (x -a)
eg - a7 +b7 or a10 + b10 is not divisible by a - b
Quadratic Equations:
Factorize-
1)x2 -3x +4 =0
2)if a+b+c =0 ,find the value of a2 +b2 +c2/a2 -bc
