One of the factors of the quadratic expression 5x2 + 7x + 2 is (5x + 1).
To find the factors, we can use the factoring method. First, multiply the coefficient of the quadratic term (5) by the constant term (2), which gives us 10. We need to find two numbers that multiply to 10 and add up to the coefficient of the linear term (7). The numbers 5 and 2 satisfy this condition since 5 × 2 = 10 and 5 + 2 = 7.
Next, we can rewrite the middle term (7x) using the found numbers:
5x2 + 5x + 2x + 2.
Now, we can group the terms:
(5x2 + 5x) + (2x + 2).
Factoring out the common factors in each group gives us:
5x(x + 1) + 2(x + 1).
Now, we can factor out the common binomial factor:
(5x + 2)(x + 1).
Therefore, one of the factors of the expression 5x2 + 7x + 2 is (5x + 1).