Question

Factor the expression. If the expression cannot be factored, say so.

Answer 1

(x + 2)(2x + 1)

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)

Answer 2

Delta = 25 - 16 = 9 =>
`√(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).