Limit. lim_(xirghtarrow 2)(3x^2 -5x-2)/(x-2)

prkosnognm 2022-07-25 Answered
Limit. lim x 2  3 x 2 5 x 2 x 2
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Answers (1)

cindysnifflesuz
Answered 2022-07-26 Author has 19 answers
I'm assuming (x-2) is all in the denominator:
lim x 2 3 x 2 5 x 2 x 2
Factor numerator:
lim x 2 ( x 2 ) ( 3 x + 1 ) x 2
lim x 2 ( 3 x + 1 ) = 3 ( 2 ) + 1 = 6
ETA: factoring steps
a x 2 + b x + c
You want two numbers that give you (a*c) and add up to b.
ac = -6
b = -5
The two numbers you want are -6 and 1.
Rewrite term "bx":
3 x 2 6 x + x 2
Factor by grouping:
( 3 x 2 6 x ) ( + x 2 )
3x(x-2)+1(x-2) [two inner parentheses should be the same]
(3x+1)(x-2)
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