Question

topic 5: factoring expressions directions: factor each expression. if it cannot be factored, write \prime.\ 28. 14x - 20 29. 32y + 56 30. 9x - 7

Explanation:

Problem 28: Factoring \( 14x - 20 \)

Step 1: Find GCF of 14 and 20

The factors of 14 are \( 1, 2, 7, 14 \), and factors of 20 are \( 1, 2, 4, 5, 10, 20 \). The greatest common factor (GCF) is \( 2 \).

Step 2: Factor out GCF

Factor out \( 2 \) from \( 14x - 20 \):
\( 14x - 20 = 2(7x - 10) \)

Step 1: Find GCF of 32 and 56

Factors of 32: \( 1, 2, 4, 8, 16, 32 \); factors of 56: \( 1, 2, 4, 7, 8, 14, 28, 56 \). GCF is \( 8 \).

Step 2: Factor out GCF

Factor out \( 8 \) from \( 32y + 56 \):
\( 32y + 56 = 8(4y + 7) \)

Check for common factors: The GCF of 9 and 7 is \( 1 \) (since 7 is prime and does not divide 9). There are no other common factors or factorable patterns (e.g., difference of squares, trinomial) here. Thus, the expression is prime.

Answer:

\( 2(7x - 10) \)

Problem 29: Factoring \( 32y + 56 \)