The problem asks to factorize the quadratic expression $2x^2 + 9x + 4$.
2025/5/10
1. Problem Description
The problem asks to factorize the quadratic expression .
2. Solution Steps
We need to factorize the quadratic expression . We are looking for two binomials of the form such that , , and .
We can try different combinations of factors for 2 and
4. Since $2$ is prime, the only factors are $1$ and $2$. The factors of $4$ are $1$ and $4$ or $2$ and $2$.
Let's try and . Then we have . We want and .
If and , then . This works.
Thus, the factors are .
Alternatively, we can use the "たすき掛け" (cross multiplication) method.
We look for two numbers that multiply to and add to . These numbers are and .
Then we rewrite the middle term:
3. Final Answer
The factored form of the expression is .