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 think the answer is 3x-4 and 2x+15

Answer 2

`\Rightarrow (2x+15)(3x-4)`

A is correct.

Explanation:

Given: The polynomial

`6x^2+37x-60`

We need to factor the polynomial using middle term splitting.

`\Rightarrow 6x^2+37x-60`

`\Rightarrow 6x^2+45x-8x-60`

Make two group

`\Rightarrow (6x^2+45x)+(-8x-60)`

Factor each group

`\Rightarrow 3x(2x+15)-4(2x+15)`

`\Rightarrow (2x+15)(3x-4)`

Hence, The factors of given polynomial is (2x+15) and (3x-4)