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

Question

(if possible).𝑦 = 𝑥2 − 6𝑥 − 27

Answer 1

To factor this quadratic equation, we need to find two numbers that multiply to -27 and add up to -6. These numbers are -9 and 3.

So, first we will rewrite the equation with common factoring:

𝑦 = 𝑥^2 - 9𝑥 + 3𝑥 - 27

Next, we will group the terms and factor out the common factors:

𝑦 = (𝑥^2 - 9𝑥) + (3𝑥 - 27)

𝑦 = 𝑥(𝑥 - 9) + 3(𝑥 - 9)

𝑦 = (𝑥 - 9)(𝑥 + 3)

Therefore, the factored form of the equation 𝑦 = 𝑥^2 − 6𝑥 − 27 is (𝑥 - 9)(𝑥 + 3).