Math / Algebra

QuestionFactoring Quiz B Factor each completely. 1) $x^{2}+9 x$

Studdy Solution

STEP 1

What is this asking? We need to rewrite the expression $x^{2} + 9x$ as a product of simpler expressions. Watch out! Don't forget to factor out everything you can!

STEP 2

1. Find the Greatest Common Factor (GCF).
2. Factor out the GCF.

STEP 3

Let's look at our expression, $x^{2} + 9x$ .
We want to find the greatest common factor (GCF), which is the largest expression that divides both terms.
What divides into both $x^{2}$ and $9x$ ?

STEP 4

Well, $x^{2}$ is the same as $x \cdot x$ , and $9x$ is the same as $3 \cdot 3 \cdot x$ .
Both terms have a factor of $x$ , so $x$ is part of our GCF!

STEP 5

The number $9$ can be broken down into $3 \cdot 3$ , but those factors aren't in the $x^{2}$ term.
So, our GCF is simply $x$ !

STEP 6

Now, we divide each term in our original expression, $x^{2} + 9x$ , by our GCF, which is $x$ .

STEP 7

First term: $x^{2} \div x = x$ .
Remember, $x^{2}$ means $x \cdot x$ , and when we divide by $x$ , we're left with just $x$ .

STEP 8

Second term: $9x \div x = 9$ .
We have $9$ multiplied by $x$ , and then divided by $x$ .
The multiplication and division by $x$ effectively divide to one, leaving us with just $9$ .

STEP 9

Now, we write our GCF multiplied by the results of our divisions.
This gives us $x(x + 9)$ .

STEP 10

Our fully factored expression is $x(x + 9)$ .

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QuestionFactoring Quiz B Factor each completely. 1) $x^{2}+9 x$

Studdy Solution

STEP 1

What is this asking? We need to rewrite the expression $x^{2} + 9x$ as a product of simpler expressions. Watch out! Don't forget to factor out everything you can!

STEP 2

1. Find the Greatest Common Factor (GCF).
2. Factor out the GCF.

STEP 3

Let's look at our expression, $x^{2} + 9x$ .
We want to find the greatest common factor (GCF), which is the largest expression that divides both terms.
What divides into both $x^{2}$ and $9x$ ?

STEP 4

Well, $x^{2}$ is the same as $x \cdot x$ , and $9x$ is the same as $3 \cdot 3 \cdot x$ .
Both terms have a factor of $x$ , so $x$ is part of our GCF!

STEP 5

The number $9$ can be broken down into $3 \cdot 3$ , but those factors aren't in the $x^{2}$ term.
So, our GCF is simply $x$ !

STEP 6

Now, we divide each term in our original expression, $x^{2} + 9x$ , by our GCF, which is $x$ .

STEP 7

First term: $x^{2} \div x = x$ .
Remember, $x^{2}$ means $x \cdot x$ , and when we divide by $x$ , we're left with just $x$ .

STEP 8

Second term: $9x \div x = 9$ .
We have $9$ multiplied by $x$ , and then divided by $x$ .
The multiplication and division by $x$ effectively divide to one, leaving us with just $9$ .

STEP 9

Now, we write our GCF multiplied by the results of our divisions.
This gives us $x(x + 9)$ .

STEP 10

Our fully factored expression is $x(x + 9)$ .

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QuestionFactoring Quiz B Factor each completely. 1) x2+9xx^{2}+9 xx2+9x

Studdy Solution

STEP 1

What is this asking? We need to rewrite the expression x2+9xx^{2} + 9xx2+9x as a product of simpler expressions. Watch out! Don't forget to factor out everything you can!

STEP 2

1. Find the Greatest Common Factor (GCF).2. Factor out the GCF.

STEP 3

Let's look at our expression, x2+9xx^{2} + 9xx2+9x.We want to find the **greatest common factor** (GCF), which is the largest expression that divides *both* terms.What divides into both x2x^{2}x2 and 9x9x9x?

STEP 4

Well, x2x^{2}x2 is the same as x⋅xx \cdot xx⋅x, and 9x9x9x is the same as 3⋅3⋅x3 \cdot 3 \cdot x3⋅3⋅x.Both terms have a factor of xxx, so xxx is part of our GCF!

STEP 5

The number 999 can be broken down into 3⋅33 \cdot 33⋅3, but those factors aren't in the x2x^{2}x2 term.So, our **GCF is simply** xxx!

STEP 6

Now, we **divide each term** in our original expression, x2+9xx^{2} + 9xx2+9x, by our **GCF**, which is xxx.

STEP 7

First term: x2÷x=xx^{2} \div x = xx2÷x=x.Remember, x2x^{2}x2 means x⋅xx \cdot xx⋅x, and when we divide by xxx, we're left with just xxx.

STEP 8

Second term: 9x÷x=99x \div x = 99x÷x=9.We have 999 multiplied by xxx, and then divided by xxx.The multiplication and division by xxx effectively divide to one, leaving us with just 999.

STEP 9

Now, we write our **GCF** multiplied by the results of our divisions.This gives us x(x+9)x(x + 9)x(x+9).

STEP 10

Our fully factored expression is x(x+9)x(x + 9)x(x+9).

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QuestionFactoring Quiz B Factor each completely. 1) $x^{2}+9 x$

What is this asking? We need to rewrite the expression $x^{2} + 9x$ as a product of simpler expressions. Watch out! Don't forget to factor out everything you can!

1. Find the Greatest Common Factor (GCF).
2. Factor out the GCF.

Let's look at our expression, $x^{2} + 9x$ .
We want to find the greatest common factor (GCF), which is the largest expression that divides both terms.
What divides into both $x^{2}$ and $9x$ ?

Well, $x^{2}$ is the same as $x \cdot x$ , and $9x$ is the same as $3 \cdot 3 \cdot x$ .
Both terms have a factor of $x$ , so $x$ is part of our GCF!

The number $9$ can be broken down into $3 \cdot 3$ , but those factors aren't in the $x^{2}$ term.
So, our GCF is simply $x$ !

Now, we divide each term in our original expression, $x^{2} + 9x$ , by our GCF, which is $x$ .

First term: $x^{2} \div x = x$ .
Remember, $x^{2}$ means $x \cdot x$ , and when we divide by $x$ , we're left with just $x$ .

Second term: $9x \div x = 9$ .
We have $9$ multiplied by $x$ , and then divided by $x$ .
The multiplication and division by $x$ effectively divide to one, leaving us with just $9$ .

Now, we write our GCF multiplied by the results of our divisions.
This gives us $x(x + 9)$ .

Our fully factored expression is $x(x + 9)$ .