Question
\( \leftarrow \quad \) Factor. Check by multiplying. \( \begin{array}{l}8 x^{5}-24 x^{3}\end{array} \)
Ask by Ayala Willis. in the United States
Feb 24,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( 8x³(x² – 3) \)
Solution
Step 1: Identify the common factors in both terms.
Both 8x⁵ and –24x³ have a common factor of 8x³.
Step 2: Factor 8x³ out of the expression.
8x⁵ – 24x³ = 8x³(x²) – 8x³(3) = 8x³(x² – 3).
Step 3: Verify by multiplying.
Multiply 8x³ by each term inside the parentheses:
8x³ · x² = 8x⁵
8x³ · (–3) = –24x³
So, the product is indeed 8x⁵ – 24x³.
Final Answer: 8x³(x² – 3)
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution The Deep Dive
To factor the expression \(8x^5 - 24x^3\), start by identifying the greatest common factor (GCF) of the terms. Here, the GCF is \(8x^3\). So, we can factor that out: \[ 8x^5 - 24x^3 = 8x^3 (x^2 - 3) \] Now, to verify our factorization, we can distribute \(8x^3\) back into the parentheses: \[ 8x^3(x^2) - 8x^3(3) = 8x^5 - 24x^3 \] This matches the original expression, confirming that our factorization is correct! So, the factored form is: \[ 8x^3 (x^2 - 3) \]
