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$23 x − 5$ is a factor of $23 x 2 + x − 53$ . What is the other factor?

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x − 3

x + 3

(3 x − 1)

(3 x + 1)

answer is B.

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Detailed Solution

A polynomial is given as

23 x 2 + x − 53

.
Now, splitting the middle term and factoring, we get,

⇒ 23 x 2 + x − 53 = 23 x 2 + 6 x − 5 x − 53 ⇒ 23 x 2 + x − 53 = 23 x x + 3 − 5 x + 3 ⇒ 23 x 2 + x − 53 = 23 x − 5 x + 3

Therefore, the factored form of

23 x 2 + x − 53

23 x − 5 x + 3

.
So, the other factor is

(x + \sqrt{3})

.
Hence, option 2 is correct.

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