Verified Answer :

crisforp

Delta = 25 - 16 = 9 => \(\sqrt{Delta} = 3;\)
\(x_{1} = (-5 + 3)/4 = -1/2 and x_{2} = (-5 -3)/4 = -2;\);
=> 2\(x^{2} + 5x + 2 = 2(x+1/2)(x+2).\) = (2x+1)(x+2).

chetankachana

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)

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