Find solutions to your questions with the help of IDNLearn.com's expert community. Ask your questions and receive prompt, detailed answers from our experienced and knowledgeable community members.

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

Factor The Expression If The Expression Cannot Be Factored Say So class=

Sagot :

Delta = 25 - 16 = 9 => [tex] \sqrt{Delta} = 3;[/tex]
[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)