Write the following equations in factored form. Remember to common factor first

Question

(if possible).𝑦 = 𝑥^2 − 6𝑥 − 27

Answer 1

First, we can look for a common factor between the three terms. We notice that they are all divisible by 3, so we can factor out a 3:
𝑦 = 3(𝑥^2 − 6𝑥 − 9)

Next, we can try to factor the quadratic expression inside the parentheses. We can use the quadratic formula or complete the square to find that:
𝑥^2 − 6𝑥 − 9 = (𝑥 − 3)^2 − 18

Substituting this back into our original equation, we get:
𝑦 = 3((𝑥 − 3)^2 − 18)

Finally, we can distribute the 3 and write the equation in factored form:
𝑦 = 3(𝑥 − 3)^2 − 54