# 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 2x 2 + 11x + 5, we take the factors

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

**Transcribed Image Text:**

## 2x² + 11x + 5 = (2x)(*C

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## We need to factor 2x 2 11x 5 In order to factor 2x 2 11x 5 we must fin…View the full answer

**Related Book For**

## Basic Technical Mathematics

**ISBN:** 9780137529896

12th Edition

**Authors:** Allyn J. Washington, Richard Evans

**Question Details**

**6**- Factoring and Fractions

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