Noahlumadue31idn
Answered

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Complete the steps to factor [tex]$2x^2 + 6x + 5x + 15$[/tex] by grouping.

Step 1: Group the first two terms and the second two terms.
[tex]\[2x^2 + 6x + 5x + 15 = (2x^2 + 6x) + (5x + 15)\][/tex]

Step 2: What is the greatest common factor of Group 1?
A. 2
B. [tex]$x$[/tex]
C. [tex]$2x$[/tex]

Step 3: What is the greatest common factor of Group 2?
A. 3
B. 5
C. [tex][tex]$5x$[/tex][/tex]

[tex]\[ (2x^2 + 6x) + (5x + 15) \][/tex]

Group 1: [tex]2x(x + 3)[/tex]
Group 2: [tex]5(x + 3)[/tex]

Sagot :

GinnyAnsweridn
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]
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