I see you are looking to solve the equation 4x + 7x^2 - 2 = 0 by factoring and then identifying the factored form of the polynomial expression. Let's go step by step:
1. Begin by rewriting the equation in standard form:
7x^2 + 4x - 2 = 0
2. To factor this quadratic equation, we need to find two numbers that multiply to -14 (product of the coefficients of x^2 and the constant term) and add up to 4 (coefficient of x). The numbers are 7 and -2.
3. Now, express the middle term (4x) using the two numbers found in the previous step:
7x^2 + 7x - 2x - 2 = 0
7x(x + 1) - 2(x + 1) = 0
4. Factor by grouping:
(7x - 2)(x + 1) = 0
5. Therefore, the factored form of the polynomial expression is (7x - 2)(x + 1).
Now, in terms of the solutions to the equation, you need to find the values of x that make the equation true. To do this, set each factor to zero and solve for x:
7x - 2 = 0
7x = 2
x = 2/7
and
x + 1 = 0
x = -1
Therefore, the solutions to the equation 7x^2 + 4x - 2 = 0 are x = 2/7 and x = -1. These are the correct solutions that you should select from the given options.
