Question
Factor the polynomial by taking out the GCF: 21p^2q^3 - 28p^4q^2
Answers
Answered by
GPT-4o mini
To factor the polynomial \( 21p^2q^3 - 28p^4q^2 \) by taking out the greatest common factor (GCF), we first need to identify the GCF of the coefficients and the variable parts.
1. **Coefficients**: The coefficients are 21 and -28. The GCF of 21 and 28 is 7.
2. **Variable \( p \)**: In \( p^2 \) and \( p^4 \), the lowest power of \( p \) is \( p^2 \).
3. **Variable \( q \)**: In \( q^3 \) and \( q^2 \), the lowest power of \( q \) is \( q^2 \).
Now, we can combine these factors:
- GCF: \( 7p^2q^2 \)
Next, we factor out the GCF from the polynomial:
\[
21p^2q^3 - 28p^4q^2 = 7p^2q^2(3q - 4p^2)
\]
So, the factored form of the polynomial is:
\[
\boxed{7p^2q^2(3q - 4p^2)}
\]
1. **Coefficients**: The coefficients are 21 and -28. The GCF of 21 and 28 is 7.
2. **Variable \( p \)**: In \( p^2 \) and \( p^4 \), the lowest power of \( p \) is \( p^2 \).
3. **Variable \( q \)**: In \( q^3 \) and \( q^2 \), the lowest power of \( q \) is \( q^2 \).
Now, we can combine these factors:
- GCF: \( 7p^2q^2 \)
Next, we factor out the GCF from the polynomial:
\[
21p^2q^3 - 28p^4q^2 = 7p^2q^2(3q - 4p^2)
\]
So, the factored form of the polynomial is:
\[
\boxed{7p^2q^2(3q - 4p^2)}
\]