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Question: factor 2n²+3n-9

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Factoring the quadratic expression $$2n^2 + 3n - 9$$ involves finding two binomials that multiply to give the original expression. Here's a step-by-step guide to help you factor it: 1. **Multiply the leading coefficient and the constant term**: The leading coefficient is $$2$$ (from $$2n^2$$), and the constant term is $$-9$$. Multiply these together: $2 \times (-9) = -18$ 2. **Find two numbers that multiply to $$-18$$ and add to the middle coefficient, $$3$$**: We need two numbers that multiply to $$-18$$ and add to $$3$$. These numbers are $$6$$ and $$-3$$ because: $6 \times (-3) = -18$ $6 - 3 = 3$ 3. **Rewrite the middle term using the two numbers found**: Rewrite $$3n$$ as $$6n - 3n$$ in the original quadratic expression: $2n^2 + 6n - 3n - 9$ 4. **Group the terms**: Group the first two terms together and the last two terms together: $(2n^2 + 6n) + (-3n - 9)$ 5. **Factor out the greatest common factor (GCF) from each group**: - From the first group, $$2n^2 + 6n$$, factor out $$2n$$: $2n(n + 3)$ - From the second group, $$-3n - 9$$, factor out $$-3$$: $-3(n + 3)$ 6. **Factor out the common binomial**: Both groups now contain the common binomial $$(n + 3)$$: $2n(n + 3) - 3(n + 3)$ 7. **Factor out $$(n + 3)$$**: $(n + 3)(2n - 3)$ So, the factored form of $$2n^2 + 3n - 9$$ is: $(n + 3)(2n - 3)$ I hope this helps! Let me know if you have any further questions.

May 24, 2024, 5:43 a.m.

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