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

Video Solution

Solution Steps

00:00 Break down the trinomial

00:03 Take out the common factor from parentheses

00:17 Reduce what's possible

00:23 Identify the coefficients

00:33 Use the roots formula to find possible solutions

00:42 Substitute appropriate values and solve to find the solutions

00:57 Calculate the squares and products

01:14 Find the 2 possible solutions (addition and subtraction)

01:17 These are the solutions, with them we'll reconstruct the trinomial

01:21 Find what zeroes each solution

01:27 These will be the factors of the trinomial

01:46 Substitute this trinomial back into the equation

01:54 And this is the solution to the problem

Step-by-Step Solution

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 $(5x+4)(x+1)$ .