Answer:
(y + 1/3)(y + 2)
Explanation:
To simplify or solve the expression, we can use different methods based on the context of the problem.
If you need to factorize the expression, you can look for two binomials that, when multiplied, result in the original expression.
In this case, the expression 3y^2 + 7y + 2 cannot be easily factored using simple integer coefficients. However, you can use the quadratic formula or complete the square to find the solutions of the quadratic equation 3y^2 + 7y + 2 = 0.
Using the quadratic formula:
The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 3, b = 7, and c = 2. Plugging these values into the quadratic formula, we get:
y = (-7 ± √(7^2 - 4(3)(2))) / (2(3))
Simplifying further gives us:
y = (-7 ± √(49 - 24)) / 6
y = (-7 ± √25) / 6
y = (-7 ± 5) / 6
So the solutions to the equation 3y^2 + 7y + 2 = 0 are:
y = (-7 + 5) / 6 = -2/6 = -1/3
and
y = (-7 - 5) / 6 = -12/6 = -2
Therefore, the expression 3y^2 + 7y + 2 can be factored as (y + 1/3)(y + 2).