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Q.

Factorize the given equation:

$2 x 3 − 3 x 2 − 17 x + 30 = 0$

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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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