Write the following equations in factored form. Remember to common factor first
(if possible).𝑦 = 𝑥 power 2 − 6𝑥 − 27
We can first try to factor out a common factor from all the terms, which in this case is 1. Then we can proceed to use factoring methods to write the equation in factored form:
𝑦 = 𝑥² - 6𝑥 - 27
𝑦 = (𝑥 - 9)(𝑥 + 3)
Therefore, the factored form of the equation 𝑦 = 𝑥² - 6𝑥 - 27 is (𝑥 - 9)(𝑥 + 3).
To factor the equation 𝑦 = 𝑥^2 - 6𝑥 - 27, let's first check if there is a common factor among the terms.
The coefficients 1, -6, and -27 do not have a common factor, so we proceed to factor the quadratic equation.
Next, we need to find two numbers that multiply to give -27 and add up to -6 (the coefficient of 𝑥). These numbers are -9 and 3.
Thus, we can rewrite the equation as 𝑦 = (𝑥 - 9)(𝑥 + 3), where (𝑥 - 9) and (𝑥 + 3) are the factored forms of the quadratic equation.