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Q.

Factorize the given equation:


2 x 3 −3 x 2 −17x+30=0  


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a

x-2x+42x-5

b

x-2x+22x-5

c

  x-2x+12x-5

d

(x-2)(x+3)(2x-5) 

answer is D.

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Detailed Solution

Concept-. To factorize the given equation by using the polynomial formula polynomial – the sum of more than one term or more than one expression is known as polynomial.
We solve this question by hit and trial method.
So,
Substitute x=2 in the given question,
We have
2 (2) 3 −3 (2) 2 −17(2)+30=0 16−12−34+30=0 46−46=0  
Then, (x-2) is the one factor.
Now, Substitute x= -3 in given question
We have,
2 (−3) 3 −3 (−3) 2 −17(−3)+30=0 −54−27+51+30=0 81−81=0  
Then, (x+3) is one factor.
Now,
Substitute x=52 in given question
We have,
2 (52) 3 −3 (52) 2 −17(52)+30=0 1250−754−1704+1204=0 2454−2454=0  
Then, (2x-5) is another factor
So the three factors are (x-2),(x+3), (2x-5)
Hence, the correct option is 4) (x-2)(x+3)(2x-5).
 
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