Question

lesson 1: factoring homework day 1
factor the gcf from each polynomial.

1. $12r^3 - 8r$
2. $16m^6 - 32m^4 + 40m^2$
3. $12x^5 + 30x^2$

Explanation:

Problem 1: \( 12r^3 - 8r \)

Step 1: Find GCF of coefficients and variables

• Coefficients: GCF of 12 and 8 is 4.
• Variables: GCF of \( r^3 \) and \( r \) is \( r \).
• So GCF is \( 4r \).

Step 2: Divide each term by GCF

\( \frac{12r^3}{4r} = 3r^2 \), \( \frac{-8r}{4r} = -2 \).

Step 3: Factor out GCF

\( 4r(3r^2 - 2) \)

Step 1: Find GCF of coefficients and variables

• Coefficients: GCF of 16, 32, 40 is 8.
• Variables: GCF of \( m^6 \), \( m^4 \), \( m^2 \) is \( m^2 \).
• So GCF is \( 8m^2 \).

Step 2: Divide each term by GCF

\( \frac{16m^6}{8m^2} = 2m^4 \), \( \frac{-32m^4}{8m^2} = -4m^2 \), \( \frac{40m^2}{8m^2} = 5 \).

Step 3: Factor out GCF

\( 8m^2(2m^4 - 4m^2 + 5) \)

Step 1: Find GCF of coefficients and variables

• Coefficients: GCF of 12 and 30 is 6.
• Variables: GCF of \( x^5 \) and \( x^2 \) is \( x^2 \).
• So GCF is \( 6x^2 \).

Step 2: Divide each term by GCF

\( \frac{12x^5}{6x^2} = 2x^3 \), \( \frac{30x^2}{6x^2} = 5 \).

Step 3: Factor out GCF

\( 6x^2(2x^3 + 5) \)

Answer:

\( 4r(3r^2 - 2) \)

Problem 2: \( 16m^6 - 32m^4 + 40m^2 \)