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

Question

(if possible).
𝑦 = 𝑥2 − 6𝑥 − 27

Answer 1

To factor 𝑦 = 𝑥2 − 6𝑥 − 27, we first look for common factors. 3 is a common factor of all three terms, since each term is divisible by 3. Therefore, we can factor out a 3:

𝑦 = 3(𝑥2 − 6𝑥 − 9)

Now we need to factor the quadratic expression inside the parentheses. To do this, we can use the quadratic formula, completing the square, or factoring by grouping. The quadratic can be factored as:

𝑦 = 3(𝑥 − 9)(𝑥 + 1)

Therefore, the factored form of 𝑦 = 𝑥2 − 6𝑥 − 27 is 𝑦 = 3(𝑥 − 9)(𝑥 + 1).