Question

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)

Answer 1

I hope this helps you

Answer 2

`\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.