Question
CF: \( 12 \mathrm{x}^{4}-16 x^{5}+24 \mathrm{x}^{3} \) Once you pull out \( 4 x^{3} \), what is left inside the parenthesis? soif you want to
Ask by Young Lane. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
After factoring out \(4x^3\), the expression inside the parentheses is \(3x - 4x^2 + 6\).
Solution
\(12x^4 - 16x^5 + 24x^3 = 4x^3\bigl(3x - 4x^2 + 6\bigr)\).
To explain step by step:
1. Divide each term by \(4x^3\):
- \(\frac{12x^4}{4x^3} = 3x\)
- \(\frac{-16x^5}{4x^3} = -4x^2\)
- \(\frac{24x^3}{4x^3} = 6\)
2. Thus, after factoring out \(4x^3\), what remains inside the parenthesis is:
\(\boxed{3x - 4x^2 + 6}\).
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Simplify this solution The Deep Dive
When you pull out \( 4 x^{3} \) from the expression \( 12 x^{4} - 16 x^{5} + 24 x^{3} \), you essentially divide each term by \( 4 x^{3} \). The first term \( 12 x^{4} \) becomes \( 3 x \), the second term \( -16 x^{5} \) becomes \( -4 x^{2} \), and the third term \( 24 x^{3} \) simplifies to \( 6 \). So, what’s left in the parentheses is \( 3x - 4x^{2} + 6 \). To put it in a neater format, your expression will look like this: \( 4 x^{3}(3x - 4x^{2} + 6) \). Now you have a clearer factorization and can rearrange or simplify further if needed!
