Question

2u2+11u+9

Answer 1

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:

1. **Identify the coefficients**:
- \( a = 2 \)
- \( b = 11 \)
- \( c = 9 \)

2. **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.

3. **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!