write the following equations in factored form. Remember to common factor first
(if possible).
𝑦 = 2𝑥2 + 3𝑥 − 2
𝑦 = (2𝑥 − 1)(𝑥 + 2)
To factor the equation 𝑦 = 2𝑥^2 + 3𝑥 - 2, we first look for common factors among the coefficients. In this case, there are no common factors among the coefficients.
Next, we need to find a pair of numbers that multiply to give the product of the leading coefficient (2) and the constant term (-2), and also add up to the coefficient of the middle term (3). These numbers are 2 and 1.
Using these numbers, we can rewrite the middle term (3𝑥) as 2𝑥 + 1𝑥:
𝑦 = 2𝑥^2 + 2𝑥 + 1𝑥 - 2
Now, we group the terms two by two:
𝑦 = (2𝑥^2 + 2𝑥) + (1𝑥 - 2)
We can factor out the common factor from the first group and second group separately:
𝑦 = 2𝑥(𝑥 + 1) + 1(𝑥 - 2)
Finally, we can rewrite the equation in factored form:
𝑦 = (2𝑥 + 1)(𝑥 - 2)