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Factor the leading coefficient from each expression. \( \begin{array}{ll}\text { 29. } \frac{1}{3} a+\frac{5}{3}=\frac{1}{3}(\square) & \text { 30. } \frac{1}{5} x-\frac{2}{5}=\frac{1}{5}(\square)\end{array} \)

Ask by Griffiths Rodriquez. in the United States
Feb 25,2025

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29. \( \frac{1}{3}(a + 5) \) 30. \( \frac{1}{5}(x - 2) \)

Solución

To factor the leading coefficient from each expression, we’ll factor out the fraction from all terms. 29. For (1/3)a + (5/3), the common factor is 1/3. Factoring 1/3 from each term gives:   1/3 · [a + 5] 30. For (1/5)x − (2/5), the common factor is 1/5. Factoring 1/5 from each term gives:   1/5 · [x − 2] Thus, the answers are: 29. 1/3(a + 5) 30. 1/5(x − 2)

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Beyond the Answer

To factor the leading coefficient from the first expression, we can take \( \frac{1}{3} \) out of the expression: \[ \frac{1}{3} a + \frac{5}{3} = \frac{1}{3} \left( a + 5 \right) \] For the second expression, we do the same: \[ \frac{1}{5} x - \frac{2}{5} = \frac{1}{5} \left( x - 2 \right) \] So, the final factored forms are: 29. \( \frac{1}{3}(a + 5) \) 30. \( \frac{1}{5}(x - 2) \)

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