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The polynomial 6x2 + 37x – 60 represents an integer. Which expressions represent integer factors of 6x2 + 37x – 60 for all values of x?

3x – 4 and 2x + 15
3x + 4 and 2x – 15
2(x – 2) and 3(x + 5)
2(x + 2) and 3(x – 5)

2 Answers

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The polynomial 6x2 + 37x – 60 represents an integer. Which expressions represent integer-example-1
User Adam Rackis
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2 votes

Answer:


\text{The integral factors are }(3x-4)(2x+15)

Explanation:

Given the quadratic polynomial


6x^2+37x-60

we have to find the integral factors of the above polynomial.


\text{The polynomial is }6x^2+37x-60

By splitting middle-term, the polynomial can be written as


6x^2+37x-60


6x^2-8x+45x-60

Taking 2x common from first two terms and 15 from last two terms.


2x(3x-4)+15(3x-4)

Taking (3x-4) common


(3x-4)(2x+15)

which are required factors of given polynomial.

Hence, option 1 is correct.

User Yeti
by
7.6k points
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