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## Sagot :

[tex] x_{1} = (-5 + 3)/4 = -1/2 and x_{2} = (-5 -3)/4 = -2;[/tex];

=> 2[tex] x^{2} + 5x + 2 = 2(x+1/2)(x+2).[/tex] = (2x+1)(x+2).

**Answer:**

(x + 2)(2x + 1)

**Step-by-step explanation:**

Hello!

We can factor this expression using the **grouping method.**

**What is the Grouping Method?**

The grouping method is a way to factor quadratic expressions and is mostly likely used when given an even number of terms. I will show you how to factor by grouping shortly.

**Step 1: AC and B**

This equation is written in the **standard form of a quadratic : **ax² + bx + c

The rule of grouping is that we need to find two factors, so that when the terms *ax²* and *c* are multipliedd together, the two factors would add to *bx.*

Using the given problem:

- ax² is 2x²
- bx is 5x
- c is 2

Multiply:

- 2(2x²)
- 4x²

That means that the two factors that multiply to 4x² should add to 5x. The terms that work is x and 4x.

**Step 2: Expand and factor **

Now we simply replace 4x and x for 5x.

- 2x² + x + 4x + 2

Now think of these one expressions as two seperate ones.

- (2x² + x) + (4x + 2)

Find the GCF in both parenthesis

- x(2x + 1) + 2(2x + 1)

Simplify

- (x + 2)(2x + 1)

Your factored equation is (x + 2)(2x + 1)