Decompose the Expression 5x^2+9x+4 into Trinomials

Decompose the following expression into trinomials

$5x^2+9x+4$

To solve the problem of factoring the quadratic expression $5x^2 + 9x + 4$, we can use the decomposition method:

• Step 1: Identify $a = 5$, $b = 9$, and $c = 4$. Calculate the product $a \cdot c = 5 \cdot 4 = 20$.
• Step 2: We need two numbers whose product is 20 and whose sum is 9. The numbers 5 and 4 satisfy this condition because $5\times4=20$ and $5+4=9$.
• Step 3: Decompose the middle term using these numbers: $5x^2 + 5x + 4x + 4$.
• Step 4: Group the terms: $(5x^2 + 5x) + (4x + 4)$.
• Step 5: Factor each group: $5x(x + 1) + 4(x + 1)$.
• Step 6: Use the distributive property to factor out the common binomial: $(5x + 4)(x + 1)$.

Therefore, the factorization of the expression $5x^2 + 9x + 4$ is $(5x+4)(x+1)$.