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

6x^2 + 37x - 60 = 6x^2 - 8x + 45x - 60 = 2x(3x - 4) + 15(3x - 4) = (3x - 4)(2x + 15)

Answer 2

For this case we have the following polynomial:

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Rewriting the polynomial in the term of degree 1 we have:

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Then, we group the expression obtained as:

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In the first parenthesis we do 2x common factor.

In the second parenthesis we make a common factor 15.

We have then:

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Then, we make a common factor of both parentheses:

`image`

Answer:

The expressions that represent integer factors of
`6x ^ 2 + 37x - 60` for all values of x are:

`image`

option 1