Write the following equations in factored form. Remember to common factor first
π¦ = 2π₯ power2 + 3π₯ β 2
π¦ = (2π₯ β 1)(π₯ + 2)
To factor the equation π¦ = 2π₯^2 + 3π₯ - 2, we'll first look for any common factors among the coefficients of the terms. In this case, there are no common factors other than 1.
Next, we'll try to factor the quadratic expression π¦ = 2π₯^2 + 3π₯ - 2 using the factoring method. The factored form of a quadratic equation can be written as the product of two binomials in the form (π₯ + π)(π₯ + π), where π and π are constants.
To find the factors, we need to determine two numbers, π and π, whose sum is equal to the coefficient of the linear term (3π₯) and whose product is equal to the product of the coefficient of the quadratic term (2π₯^2) and the constant term (-2). In this case, we have:
Coefficient of the linear term: 3π₯
Coefficient of the quadratic term: 2π₯^2
Constant term: -2
We need to find numbers π and π such that π + π = 3 and ππ = (2π₯^2)(-2).
Considering the values of π and π, we observe that the pair of numbers that satisfies these conditions is π = 2 and π = -1, as 2 + (-1) = 3 and 2(-1) = -2.
Therefore, we can factor the quadratic equation as:
π¦ = 2π₯^2 + 3π₯ - 2
π¦ = (π₯ + 2)(π₯ - 1)
So, the factored form of the equation π¦ = 2π₯^2 + 3π₯ - 2 is (π₯ + 2)(π₯ - 1).