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Question: factor 5x²-18x+9

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To factor the quadratic expression $$5x² - 18x + 9$$, follow these steps: 1. **Identify the coefficients**: The quadratic expression is in the form $$ax² + bx + c$$, where $$a = 5$$, $$b = -18$$, and $$c = 9$$. 2. **Multiply $$a$$ and $$c$$**: $$a \times c = 5 \times 9 = 45$$. 3. **Find two numbers that multiply to $$ac$$ and add up to $$b$$**: We need to find two numbers whose product is 45 and whose sum is -18. These numbers are -3 and -15 because: $$-3 \times -15 = 45$$ $$-3 + (-15) = -18$$. 4. **Rewrite the middle term ($$bx$$) using these two numbers**: Rewrite $$-18x$$ as $$-3x - 15x$$: $5x² - 3x - 15x + 9$ 5. **Group the terms in pairs**: $(5x² - 3x) + (-15x + 9)$ 6. **Factor out the greatest common factor (GCF) from each pair**: From $$5x² - 3x$$, factor out $$x$$: $x(5x - 3)$ From $$-15x + 9$$, factor out $$-3$$: $-3(5x - 3)$ 7. **Factor by grouping**: Now the expression looks like this: $x(5x - 3) - 3(5x - 3)$ Notice that $$(5x - 3)$$ is a common factor: $(5x - 3)(x - 3)$ Therefore, the factored form of $$5x² - 18x + 9$$ is: $(5x - 3)(x - 3)$

May 24, 2024, 5:52 a.m.

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