Factorization - Common Factor: Identifying a Common Factor of a number following decomposition

To find the common factor of the expression $4y+4$, we need to factor each term. The expression can be rewritten as:

$4\cdot y + 4\cdot 1$

The number 4 is common in both terms, as we can see: $\orange4\cdot y + \orange4\cdot 1$ .

Hence, the common factor is $4$.

To find the common factor of the expression $5x + 10$, we need to look at the coefficients and constants.

The expression $5x + 10$ can be rewritten as $5 \cdot x + 5 \cdot 2$.

This shows that each term contains the factor $5$, as we can see it shows up in both of the terms: $\orange5 \cdot x + \orange5 \cdot 2$.

Therefore, the common factor is $5$.

To find the common factor of the expression $5z+5$, we need to factor each term. The expression can be rewritten as:

$5\cdot z + 5\cdot 1$

The number 5 is common in both terms, as we can see: $\orange 5\cdot z + \orange5\cdot 1$.

Hence, the common factor is $5$.

To find the common factor of the expression $7x + 14$, we need to look at the coefficients and constants.

The expression $7x + 14$ can be rewritten as $7 \cdot x + 7 \cdot 2$.

This shows that each term contains the factor $7$, as both terms contains it: $\orange 7 \cdot x + \orange 7 \cdot 2$ .

Therefore, the common factor is $7$.

First, consider the expression $3x^2+9x$. We want to factor out the greatest common factor of the terms.

Both terms, $3x^2$ and $9x$, contain the factor$x$. Therefore, $x$ is a common factor.

Write each term showing the factor $x$: $3\cdot x\cdot\orange x$ and $9\cdot\orange x$.

However, we can further more factor the number $9$, to $3\cdot3$.

So, we can see there's another common factor,$3$, as we can see in both terms: $\blue3\cdot x\cdot x$ and $\blue3\cdot3\cdot x$.

$\blue3\cdot x\cdot\orange x$ and $\blue 3\cdot3\cdot \orange x$

The greatest common factor is then $3x$.

First, consider the expression $4x^2+3x$. We want to factor out the greatest common factor of the terms.

Both terms, $4x^2$ and $3x$, contain the factor $x$. Therefore, $x$ is a common factor.

Write each term showing the factor $x$: $4\cdot x\cdot \orange x$ and $3\cdot \orange x$.

The greatest common factor is $x$.

First, consider the expression $5x^2+10x$. We want to factor out the greatest common factor of the terms.

Write each term showing the factor $x$: $\blue 5\cdot \orange x\cdot x$ and $2\cdot\blue5\cdot \orange x$.

Both terms, $5x^2$ and $10x$, contain the factor $x$ as well as $5$. Therefore, $5\cdot x$ is a common factor.

The greatest common factor is $5\cdot x$.

To factor the expression $5y^2+9y$, we first write each term as a product of factors:

$5y^2 = 5 \cdot y \cdot \orange y$ and $9y=9\cdot \orange y$.

We notice that both terms include the factor $y$. Thus, the common factor is $y$.

First, consider the expression $6x^2+8x$. We want to factor out the greatest common factor of the terms.

Both terms, $6x^2$ and $8x$, contain the factor $x$. Therefore, $x$ is a common factor.

But we can keep factoring the numbers as well. $6$ can be factored to $2\cdot3$, and$8$ can be factored to $2\cdot4$.

Write each term showing the factor $x$: $\blue2\cdot3\cdot \orange x\cdot x$ and $\blue 2\cdot4\cdot \orange x$.

Therefore, the greatest common factor is $2\cdot x$.

To factor the expression $z^2+9z$, we write each term as a product of factors:

$z^2=z\cdot \orange z$ and $9z = 9 \cdot \orange z$.

We observe that both terms have a common factor of $z$, so the greatest factor is $z$.

First, identify the coefficients and the terms in the expression $5x + 10$.

Break down each term:

$5x$ can be written as $5 \cdot x$.

$10$ can be written as $5 \cdot 2$.

The common factor of these two terms is $5$.

Therefore, the factored form of the expression is $5(x + 2)$, and the common factor is $5$.

Consider the expression $2y + 4$.

Decompose each term into factors:

$2y$ can be rewritten as $2 \cdot y$.

$4$ can be rewritten as $2 \cdot 2$.

The common factor of these terms is $2$.

This means you can factor the expression as $2(y + 2)$. Therefore, the common factor is $2$.