write the following equations in factored form. Remember to common factor first

Question

(if possible).
𝑦 = 2𝑥power2 + 3𝑥 − 2

Answer 1

We first look for common factors, but there are none. Therefore, we proceed to factor the quadratic equation using the quadratic formula or by factoring by grouping:

𝑦 = 2𝑥² + 3𝑥 − 2

Using the quadratic formula:

𝑥 = [−(3) ± √(3² − 4(2)(−2))]/(2(2))
𝑥 = [−3 ± √(25)]/4
𝑥 = [−3 ± 5]/4

Thus, the solutions are:

𝑥 = −1/2 or 𝑥 = 2

Therefore, the factored form of the equation is:

𝑦 = 2(𝑥 + 1/2)(𝑥 − 2)