Question

factor each expression.

1. $3x + 15$
2. $2x + 10$
3. $4x - 28$
4. $5x - 15$

state whether the expressions are equivalent or not equivalent.

Explanation:

Problem 5: Factor \( 3x + 15 \)

Step 1: Identify the GCF

The greatest common factor (GCF) of \( 3x \) and \( 15 \) is \( 3 \).

Step 2: Factor out the GCF

Divide each term by \( 3 \): \( \frac{3x}{3} + \frac{15}{3} = x + 5 \). Then, write the expression as the product of the GCF and the resulting polynomial: \( 3(x + 5) \).

Step 1: Identify the GCF

The GCF of \( 2x \) and \( 10 \) is \( 2 \).

Step 2: Factor out the GCF

Divide each term by \( 2 \): \( \frac{2x}{2} + \frac{10}{2} = x + 5 \). Then, write the expression as \( 2(x + 5) \).

Step 1: Identify the GCF

The GCF of \( 4x \) and \( 28 \) is \( 4 \).

Step 2: Factor out the GCF

Divide each term by \( 4 \): \( \frac{4x}{4} - \frac{28}{4} = x - 7 \). Then, write the expression as \( 4(x - 7) \).

Answer:

\( 3(x + 5) \)

Problem 6: Factor \( 2x + 10 \)