find a and b if X + 1 X + 2 is a factor of x cube + 3 x square - 2 X + b
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Given
(x+1), (x+2) are factors of polynomial x^3+3x^2-2ax+b
To Find
a=? , b=?
Let p(x)=x^3+3 x^2-2ax+b
By factor theorem
p(-1)=(-1)^3+3(-1)^2-2a(-1)+b=0
-1+3+2a+b=0
-2+2a+b=0
2a+b=2
2a=2-b ➡(1)
p(-2)=(-2)^3+3(-2)^2-2a(-2)+b=0
-8+12+4a+b=0
4+4a+b=0
4+2(2a)+b=0
4+2(2-b)+b=0 [since from (1)]
4+4-2b+b=0
8-b=0
b=8
Substitute b=8 in eq-(1)
2a=2-b
2a=2-8
2a=-6
a=-3
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