assignment
factor the common factor out of each expression.
1) $-25x^3 - 20x^4$
2) $12x^8 + 9x^4$
3) $35x^5u - 28x^4u^2 + 14x^4$
4) $-50y^3x^2 + 20y^4x + 30y^4$
5) $8mn^4 + 20m^2n^2 + 16mn - 16m$
6) $60x^2y + 30xy^2 + 12x^2y + 18xy$

Question

Accepted Answer

### Problem 1: $-25x^{3}-20x^{4}$
# Explanation:
## Step 1: Identify the GCF of coefficients and variables
The GCF of $-25$ and $-20$ is $5$ (we take the negative sign for the common factor to make the leading term positive, so $-5$). For the variables, the GCF of $x^{3}$ and $x^{4}$ is $x^{3}$. So the common factor is $-5x^{3}$.
## Step 2: Factor out the common factor
$-25x^{3}-20x^{4}=-5x^{3}(5 + 4x)$
# Answer: $-5x^{3}(5 + 4x)$

### Problem 2: $12x^{8}+9x^{4}$
# Explanation:
## Step 1: Find the GCF of coefficients and variables
GCF of $12$ and $9$ is $3$. GCF of $x^{8}$ and $x^{4}$ is $x^{4}$. So common factor is $3x^{4}$.
## Step 2: Factor out the common factor
$12x^{8}+9x^{4}=3x^{4}(4x^{4}+3)$
# Answer: $3x^{4}(4x^{4}+3)$

### Problem 3: $35x^{5}u - 28x^{4}u^{2}+14x^{4}$
# Explanation:
## Step 1: Determine the GCF
GCF of $35$, $-28$, and $14$ is $7$. GCF of $x^{5}u$, $x^{4}u^{2}$, and $x^{4}$ is $x^{4}$. So common factor is $7x^{4}$.
## Step 2: Factor out the common factor
$35x^{5}u - 28x^{4}u^{2}+14x^{4}=7x^{4}(5xu - 4u^{2}+2)$
# Answer: $7x^{4}(5xu - 4u^{2}+2)$

### Problem 4: $-50y^{3}x^{2}+20y^{4}x + 30y^{4}$
# Explanation:
## Step 1: Find the GCF
GCF of $-50$, $20$, and $30$ is $10$ (we take $-10y^{3}$ to make the first term positive). GCF of $y^{3}x^{2}$, $y^{4}x$, and $y^{4}$ is $y^{3}$. So common factor is $-10y^{3}$.
## Step 2: Factor out the common factor
$-50y^{3}x^{2}+20y^{4}x + 30y^{4}=-10y^{3}(5x^{2}-2yx - 3y)$
# Answer: $-10y^{3}(5x^{2}-2yx - 3y)$

### Problem 5: $8mn^{4}+20m^{2}n^{2}+16mn - 16m$
# Explanation:
## Step 1: Identify the GCF
GCF of $8$, $20$, $16$, and $-16$ is $4$. GCF of $mn^{4}$, $m^{2}n^{2}$, $mn$, and $m$ is $m$. So common factor is $4m$.
## Step 2: Factor out the common factor
$8mn^{4}+20m^{2}n^{2}+16mn - 16m = 4m(2n^{4}+5mn^{2}+4n - 4)$
# Answer: $4m(2n^{4}+5mn^{2}+4n - 4)$

### Problem 6: $60x^{2}y+30xy^{2}+12x^{2}y + 18xy$
# Explanation:
## Step 1: Combine like terms (first and third terms)
$60x^{2}y+12x^{2}y=72x^{2}y$, so the expression becomes $72x^{2}y+30xy^{2}+18xy$
## Step 2: Find the GCF
GCF of $72$, $30$, and $18$ is $6$. GCF of $x^{2}y$, $xy^{2}$, and $xy$ is $xy$. So common factor is $6xy$.
## Step 3: Factor out the common factor
$72x^{2}y+30xy^{2}+18xy=6xy(12x + 5y+3)$
# Answer: $6xy(12x + 5y + 3)$

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QUESTION IMAGE

Question

Explanation:

Problem 1: \(-25x^{3}-20x^{4}\)

Step 1: Identify the GCF of coefficients and variables

Step 2: Factor out the common factor

Step 1: Find the GCF of coefficients and variables

Step 2: Factor out the common factor

Step 1: Determine the GCF

Step 2: Factor out the common factor

Answer:

Problem 2: \(12x^{8}+9x^{4}\)