Write the following equations in factored form. Remember common factors first
(if possible). π¦ = 2π₯power2 + 3π₯ β 2
π¦ = (2π₯ β 1)(π₯ + 2)
To factor the equation π¦ = 2π₯^2 + 3π₯ - 2, we can look for common factors first, if possible.
Step 1: Check for common factors.
In this case, there are no common factors among the coefficients of the terms.
Step 2: Factor the quadratic term, if possible.
The quadratic term is 2π₯^2. Since the coefficient is not a perfect square and the quadratic cannot be factored using integer factors, we can move on to step 3.
Step 3: Look for factors of the constant term that add up to the coefficient of the linear term.
The constant term is -2. We need to find two numbers that multiply to -2 and add up to 3. The numbers that satisfy this condition are 4 and -1.
Step 4: Rewrite the equation using the factored form.
π¦ = (π₯ + 4)(π₯ - 1)
Therefore, the equation π¦ = 2π₯^2 + 3π₯ - 2 is factored as π¦ = (π₯ + 4)(π₯ - 1).