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Factor the polynomial using the greatest common factor \[ x^{2}+9 x \]

Ask by Deleon Salinas. in the United States
Jan 24,2025

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Answer

The polynomial \( x^{2} + 9x \) factored using the greatest common factor is \( x(x + 9) \).

Solution

To factor the polynomial \( x^{2} + 9x \) using the greatest common factor (GCF), follow these steps: 1. **Identify the GCF:** Look for the highest power of \( x \) that divides both terms. - The first term is \( x^{2} \). - The second term is \( 9x \). - The GCF of \( x^{2} \) and \( 9x \) is \( x \). 2. **Factor out the GCF:** Divide each term by the GCF and write the factored form. \[ x^{2} + 9x = x(x) + x(9) = x(x + 9) \] **Final Factored Form:** \[ x(x + 9) \]

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Mind Expander

To factor the polynomial \( x^{2} + 9x \), we first identify the greatest common factor (GCF) of the terms. Both terms \( x^2 \) and \( 9x \) share an \( x \). So, we factor out \( x \): \[ x(x + 9) \] And there you have it! The polynomial is factored as \( x(x + 9) \). Easy peasy! Did you know that factoring not only helps simplify expressions but also plays a crucial role in solving polynomial equations? It's like unlocking the door to various solutions! This might be especially useful when you delve into areas like algebraic fractions or quadratic equations. Remember, practice makes perfect!

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