Asked by pp
Factor the expression completely.
24, x, to the power 4 , plus, 56, x, cubed
24x
4
+56x
3
24, x, to the power 4 , plus, 56, x, cubed
24x
4
+56x
3
Answers
Answered by
GPT-4o mini
To factor the expression \( 24x^4 + 56x^3 \) completely, we can follow these steps:
1. **Find the greatest common factor (GCF)** of the coefficients (24 and 56) and the variable part (\(x^4\) and \(x^3\)):
- The GCF of 24 and 56 is 8.
- The GCF of \(x^4\) and \(x^3\) is \(x^3\).
Therefore, the overall GCF is \(8x^3\).
2. **Factor out the GCF**:
\[
24x^4 + 56x^3 = 8x^3(3x + 7)
\]
3. **Check if \(3x + 7\) can be factored further**:
The expression \(3x + 7\) is a linear polynomial and cannot be factored further.
Thus, the completely factored form of the expression \(24x^4 + 56x^3\) is:
\[
\boxed{8x^3(3x + 7)}
\]
1. **Find the greatest common factor (GCF)** of the coefficients (24 and 56) and the variable part (\(x^4\) and \(x^3\)):
- The GCF of 24 and 56 is 8.
- The GCF of \(x^4\) and \(x^3\) is \(x^3\).
Therefore, the overall GCF is \(8x^3\).
2. **Factor out the GCF**:
\[
24x^4 + 56x^3 = 8x^3(3x + 7)
\]
3. **Check if \(3x + 7\) can be factored further**:
The expression \(3x + 7\) is a linear polynomial and cannot be factored further.
Thus, the completely factored form of the expression \(24x^4 + 56x^3\) is:
\[
\boxed{8x^3(3x + 7)}
\]
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