Make the given changes in the indicated examples of this section and then factor.

In Example 3, change the + before 11x to −.

Data from Example 3

To factor 2x² + 11x + 5, we take the factors of 2 to be +2 and +1 (we use only positive coefficients a and c when the coefficient of x 2 is positive). We set up the factoring as

Because the product of the integers to be found is +5, only integers of the same sign need to be considered. [Also because the sum of the outer and inner products is +11, the integers are positive.] The factors of +5 are +1 and +5, and −1 and −5, which means that +1 and +5 is the only possible pair. Now, trying the factors

we see that 7x is not the correct middle term.

Therefore, we now try

and we have the correct sum of +11x. Therefore, 2x ² + 11x + 5 = (2x + 1)(x + 5)

For a trinomial with a first term 2x² and a constant +5 to be factorable, we can now see that the middle term must be either ±11x or ±7x. This means that 2x² + 7x + 5 = (2x + 5)(x + 1), but a trinomial such as 2x² + 8x + 5 is not factorable.

2x + 11x + 5 = (2x)(*C