To factor [tex]\(2x^2 + 6x + 5x + 15\)[/tex] by grouping, let's follow the steps mentioned:
### Step 1
Group the first two terms and the second two terms:
[tex]\[ (2x^2 + 6x) + (5x + 15) \][/tex]
### Step 2
Identify the greatest common factor (GCF) of each group:
- Group 1: [tex]\(2x^2 + 6x\)[/tex]
- The GCF is [tex]\(2x\)[/tex].
- Group 2: [tex]\(5x + 15\)[/tex]
- The GCF is [tex]\(5\)[/tex].
### Step 3
Factor out the GCF from each group:
- Group 1: [tex]\(2x^2 + 6x\)[/tex]
- Factor out [tex]\(2x\)[/tex]:
[tex]\[ 2x(x + 3) \][/tex]
- Group 2: [tex]\(5x + 15\)[/tex]
- Factor out [tex]\(5\)[/tex]:
[tex]\[ 5(x + 3) \][/tex]
Now, rewrite the original expression with the factored groups:
[tex]\[ 2x(x + 3) + 5(x + 3) \][/tex]
### Step 4
Note that both terms now have a common binomial factor [tex]\((x + 3)\)[/tex]. Factor out this common binomial factor:
[tex]\[ (2x + 5)(x + 3) \][/tex]
So, the factored form of the expression [tex]\(2x^2 + 6x + 5x + 15\)[/tex] is:
[tex]\[ (2x + 5)(x + 3) \][/tex]
