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

Question

(if possible).
𝑦 = 2𝑥2 + 3𝑥 − 2

Answer 1

First, we look for a common factor. In this case, we can factor out 2:

𝑦 = 2𝑥2 + 3𝑥 − 2
𝑦 = 2(𝑥2 + (3/2)𝑥 − 1)

Next, we need to factor the quadratic expression inside the parentheses. We can use the quadratic formula or factoring by grouping:

𝑥2 + (3/2)𝑥 − 1 = (𝑥 + 1)(𝑥 − 1/2)

Substituting this back into the original equation, we get:

𝑦 = 2(𝑥 + 1)(𝑥 − 1/2)