Question
\( 24 x ^ { 3 } + 3 x ^ { 2 } = 3 x ^ { 2 } ( \square ) \)
Ask by Peterson Powers. in the United States
Mar 03,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The expression inside the square is \(8x + 1\).
Solution
To factor the expression 24x³ + 3x², first notice that both terms have a common factor of 3x². Factoring 3x² out, we have:
24x³ + 3x² = 3x²(8x + 1).
Thus, the expression in the square is 8x + 1.
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Simplify this solution Bonus Knowledge
To complete the equation, you can factor out the common term \( 3x^2 \) from each part of the left side. So, we have: \( 3x^2 (8x + 1) \) This shows that the expression can be simplified to \( 3x^2 (8x + 1) = 0 \). This factored form is very useful because it allows you to find the roots of the equation by setting each factor to zero. In terms of real-world applications, factoring polynomials is not just an academic exercise! Engineers and architects often utilize polynomial equations to calculate forces and loads in structures. Understanding how to manipulate these expressions can lead to better design choices, efficiency, and safety in real-life building projects.
