write the following equations in factored form. Remember to common factor first
(if possible).
𝑦 = 2𝑥^2 + 3𝑥 − 2
𝑦 = (𝑥 + 2)(2𝑥 − 1)
To factor the equation 𝑦 = 2𝑥^2 + 3𝑥 − 2, we need to look for common factors first. However, there are no common factors among the terms.
To factor the quadratic expression, we need to find two numbers that multiply to give the product of the coefficient of the quadratic term (2) and the constant term (-2) while adding up to the coefficient of the linear term (3).
Let's find the factors of 2 and -2:
Factors of 2: 1, 2
Factors of -2: -1, -2
Now, let's check the possible combinations of the factors to see if any of them adds up to 3:
1 + (-2) = -1 (not equal to 3)
2 + (-1) = 1 (not equal to 3)
Since neither combination adds up to 3, we cannot factor the equation further using simple integers.
Therefore, the factored form of the equation 𝑦 = 2𝑥^2 + 3𝑥 − 2 is 𝑦 = 2𝑥^2 + 3𝑥 − 2.