Math / Algebra

QuestionFactor by grouping: $x^{2}+10 x+4 x+40$ $\square$ Question Help: ⓐ $V_{i d e}$ Submit question ${ }^{\text {Message instructor }}$

Studdy Solution

STEP 1

What is this asking? We're asked to rewrite the expression $x^2 + 10x + 4x + 40$ as a product of two factors. Watch out! Don't forget to look for the greatest common factor in each group!

STEP 2

1. Group the terms
2. Factor out the GCF from each group
3. Factor out the common binomial

STEP 3

Alright, let's group the first two terms and the last two terms together!
This gives us $(x^2 + 10x) + (4x + 40)$ .
This sets us up perfectly to find those common factors!

STEP 4

Now, let's look at the first group, $(x^2 + 10x)$ .
What's the greatest common factor here?
It's $x$ !
So, we factor out $x$ to get $x(x + 10)$ .
Awesome!

STEP 5

Next up, the second group, $(4x + 40)$ .
The greatest common factor here is $4$ !
Factoring out $4$ gives us $4(x + 10)$ .
Look at that, we have a matching binomial!

STEP 6

Putting it all together, we now have $x(x + 10) + 4(x + 10)$ .
We're so close!

STEP 7

Notice that both terms have the common factor $(x + 10)$ .
Let's factor that out!
Think of it like this: if we had $xa + 4a$ , we could factor out the $a$ to get $a(x+4)$ , right?
Same idea here!
We factor out $(x + 10)$ to get $(x + 10)(x + 4)$ .
Boom!

STEP 8

The factored expression is $(x + 10)(x + 4)$ .

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QuestionFactor by grouping: $x^{2}+10 x+4 x+40$ $\square$ Question Help: ⓐ $V_{i d e}$ Submit question ${ }^{\text {Message instructor }}$

Studdy Solution

STEP 1

What is this asking? We're asked to rewrite the expression $x^2 + 10x + 4x + 40$ as a product of two factors. Watch out! Don't forget to look for the greatest common factor in each group!

STEP 2

1. Group the terms
2. Factor out the GCF from each group
3. Factor out the common binomial

STEP 3

Alright, let's group the first two terms and the last two terms together!
This gives us $(x^2 + 10x) + (4x + 40)$ .
This sets us up perfectly to find those common factors!

STEP 4

Now, let's look at the first group, $(x^2 + 10x)$ .
What's the greatest common factor here?
It's $x$ !
So, we factor out $x$ to get $x(x + 10)$ .
Awesome!

STEP 5

Next up, the second group, $(4x + 40)$ .
The greatest common factor here is $4$ !
Factoring out $4$ gives us $4(x + 10)$ .
Look at that, we have a matching binomial!

STEP 6

Putting it all together, we now have $x(x + 10) + 4(x + 10)$ .
We're so close!

STEP 7

Notice that both terms have the common factor $(x + 10)$ .
Let's factor that out!
Think of it like this: if we had $xa + 4a$ , we could factor out the $a$ to get $a(x+4)$ , right?
Same idea here!
We factor out $(x + 10)$ to get $(x + 10)(x + 4)$ .
Boom!

STEP 8

The factored expression is $(x + 10)(x + 4)$ .

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QuestionFactor by grouping: x2+10x+4x+40x^{2}+10 x+4 x+40x2+10x+4x+40 □\square□ Question Help: ⓐ VideV_{i d e}Vide​ Submit question Message instructor { }^{\text {Message instructor }}Message instructor

Studdy Solution

STEP 1

What is this asking? We're asked to rewrite the expression x2+10x+4x+40x^2 + 10x + 4x + 40x2+10x+4x+40 as a product of two factors. Watch out! Don't forget to look for the greatest common factor in each group!

STEP 2

1. Group the terms2. Factor out the GCF from each group3. Factor out the common binomial

STEP 3

Alright, let's **group** the first two terms and the last two terms together!This gives us (x2+10x)+(4x+40)(x^2 + 10x) + (4x + 40)(x2+10x)+(4x+40).This sets us up perfectly to find those **common factors**!

STEP 4

Now, let's look at the **first group**, (x2+10x)(x^2 + 10x)(x2+10x).What's the **greatest common factor** here?It's xxx!So, we **factor** out xxx to get x(x+10)x(x + 10)x(x+10).Awesome!

STEP 5

Next up, the **second group**, (4x+40)(4x + 40)(4x+40).The **greatest common factor** here is 444!Factoring out 444 gives us 4(x+10)4(x + 10)4(x+10).Look at that, we have a **matching binomial**!

STEP 6

Putting it all together, we now have x(x+10)+4(x+10)x(x + 10) + 4(x + 10)x(x+10)+4(x+10).We're so close!

STEP 7

STEP 8

The factored expression is (x+10)(x+4)(x + 10)(x + 4)(x+10)(x+4).

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionFactor by grouping: $x^{2}+10 x+4 x+40$ $\square$ Question Help: ⓐ $V_{i d e}$ Submit question ${ }^{\text {Message instructor }}$

What is this asking? We're asked to rewrite the expression $x^2 + 10x + 4x + 40$ as a product of two factors. Watch out! Don't forget to look for the greatest common factor in each group!

1. Group the terms
2. Factor out the GCF from each group
3. Factor out the common binomial

Alright, let's group the first two terms and the last two terms together!
This gives us $(x^2 + 10x) + (4x + 40)$ .
This sets us up perfectly to find those common factors!

Now, let's look at the first group, $(x^2 + 10x)$ .
What's the greatest common factor here?
It's $x$ !
So, we factor out $x$ to get $x(x + 10)$ .
Awesome!

Next up, the second group, $(4x + 40)$ .
The greatest common factor here is $4$ !
Factoring out $4$ gives us $4(x + 10)$ .
Look at that, we have a matching binomial!

Putting it all together, we now have $x(x + 10) + 4(x + 10)$ .
We're so close!

The factored expression is $(x + 10)(x + 4)$ .