Write the following equations in factored form. Remember to common factor first
(if possible).𝑦 = 𝑥2 − 6𝑥 − 27
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).
To factor the equation 𝑦 = 𝑥^2 − 6𝑥 − 27, we can start by looking for a common factor among the coefficients of the terms. In this case, there is no common factor.
To factor the quadratic expression, we can use the factoring method or the quadratic formula. Let's use the factoring method:
We need to find two numbers whose product is -27 and whose sum is -6 (the coefficient of 𝑥). After trying different combinations, we can factor the expression as:
𝑦 = (𝑥 − 9)(𝑥 + 3)
So, the equation 𝑦 = 𝑥^2 − 6𝑥 − 27 in factored form is 𝑦 = (𝑥 − 9)(𝑥 + 3).