Question
\( \leftarrow \begin{array}{l}\text { Factor. } \\ 6 a^{2}+11 a-35\end{array} \)
Ask by Mills Bowers. in the United States
Feb 24,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( 6a^{2} + 11a - 35 = (2a + 7)(3a - 5) \)
Solution
To factor the quadratic 6a² + 11a − 35, follow these steps:
1. Multiply the coefficient of a² by the constant term: 6 × (−35) = −210.
2. Find two numbers that multiply to −210 and add to the middle coefficient, 11. The numbers 21 and −10 work since 21 × (−10) = −210 and 21 + (−10) = 11.
3. Rewrite the middle term using these numbers:
6a² + 21a − 10a − 35.
4. Group the terms:
(6a² + 21a) + (−10a − 35).
5. Factor each group:
3a(2a + 7) − 5(2a + 7).
6. Notice that (2a + 7) is common, so factor it out to get:
(2a + 7)(3a − 5).
Thus, the factored form of 6a² + 11a − 35 is (2a + 7)(3a − 5).
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Simplify this solution Extra Insights
To factor the quadratic expression \(6a^{2}+11a-35\), we are looking for two numbers that multiply to \(6 \cdot (-35) = -210\) and add up to \(11\). Those numbers are \(21\) and \(-10\). Now, we can rewrite the expression: \(6a^{2}+21a-10a-35\). Grouping the terms gives us: \(3a(2a + 7) - 5(2a + 7)\). Thus, we can factor by grouping: \((3a - 5)(2a + 7)\). Now you have the factored form as \((3a - 5)(2a + 7)\)!
