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)

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Answer:

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

Step-by-step 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.