Question
which of the following is the gcf of the polynomial 4x^4+12x^3-36x^2+24x
Answers
Answered by
GPT-4o mini
To find the greatest common factor (GCF) of the polynomial \( 4x^4 + 12x^3 - 36x^2 + 24x \), we can follow these steps:
1. **Factor out the coefficients**: Start by examining the numerical coefficients \( 4, 12, -36, \) and \( 24 \).
- The GCF of these numbers is \( 4 \).
2. **Factor out the variable part**: Next, look at the variable \( x \):
- The smallest power of \( x \) present in all terms is \( x \) (since the lowest degree term is \( x^1 \)).
3. **Combine the GCFs**: Therefore, the GCF of the polynomial is \( 4x \).
Now, let's confirm this by factoring \( 4x \) out of the polynomial:
\[
4x^4 + 12x^3 - 36x^2 + 24x = 4x(x^3 + 3x^2 - 9x + 6)
\]
Thus, the GCF of the polynomial \( 4x^4 + 12x^3 - 36x^2 + 24x \) is \( \boxed{4x} \).
1. **Factor out the coefficients**: Start by examining the numerical coefficients \( 4, 12, -36, \) and \( 24 \).
- The GCF of these numbers is \( 4 \).
2. **Factor out the variable part**: Next, look at the variable \( x \):
- The smallest power of \( x \) present in all terms is \( x \) (since the lowest degree term is \( x^1 \)).
3. **Combine the GCFs**: Therefore, the GCF of the polynomial is \( 4x \).
Now, let's confirm this by factoring \( 4x \) out of the polynomial:
\[
4x^4 + 12x^3 - 36x^2 + 24x = 4x(x^3 + 3x^2 - 9x + 6)
\]
Thus, the GCF of the polynomial \( 4x^4 + 12x^3 - 36x^2 + 24x \) is \( \boxed{4x} \).