It seems like you are working with a quadratic expression in terms of \( u \). The expression you provided is:
\[ 2u^2 + 11u + 9 \]
If you are looking to factor this quadratic expression, we can proceed as follows:
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Identify the coefficients:
- \( a = 2 \)
- \( b = 11 \)
- \( c = 9 \)
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Factor the expression: We need to find two numbers that multiply to \( a \cdot c = 2 \cdot 9 = 18 \) and add up to \( b = 11 \). The numbers 2 and 9 fit this criteria.
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Rewrite and factor by grouping: \[ 2u^2 + 2u + 9u + 9 \] Now, group the terms: \[ (2u^2 + 2u) + (9u + 9) \] Factor out the common terms from each group: \[ 2u(u + 1) + 9(u + 1) \] Now factor out the common binomial factor \((u + 1)\): \[ (2u + 9)(u + 1) \]
Thus, the factored form of the quadratic expression \( 2u^2 + 11u + 9 \) is:
\[ (2u + 9)(u + 1) \]
If you need any other assistance with this expression (like finding its roots or completing the square), let me know!