Question
Factor by grouping. \[ 3 y^{3}-5 y^{2}+15 y-25 \]
Ask by Hilton Ingram. in the United States
Mar 14,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The expression \(3y^{3}-5y^{2}+15y-25\) factors to \((3y-5)(y^{2}+5)\).
Solution
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The Deep Dive
To factor the expression \(3y^{3}-5y^{2}+15y-25\) by grouping, we start by grouping the terms: \[ (3y^3 - 5y^2) + (15y - 25) \] Now, factor out the common factors from each group: \[ y^2(3y - 5) + 5(3y - 5) \] Next, we notice that \(3y - 5\) is a common factor in both groups, so we can factor it out: \[ (3y - 5)(y^2 + 5) \] Thus, the factored form of the expression is: \[ (3y - 5)(y^2 + 5) \]
