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:

$6x ^ 2 + 37x - 60$

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

$6x ^ 2 + 37x - 60 = 6x ^ 2 - 8x + 45x - 60$

Then, we group the expression obtained as:

$(6x ^ 2 - 8x) + (45x - 60)$

In the first parenthesis we do 2x common factor.

In the second parenthesis we make a common factor 15.

We have then:

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

Then, we make a common factor of both parentheses:

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

Answer:

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

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

option 1