3. Write the following equations in factored form. Remember to common factor first
(if possible).
a) 𝑦 = 6𝑥 + 42
𝑦 = 6(𝑥 + 7)
b) 𝑦 = 𝑥^2 − 5𝑥 − 6
𝑦 = (𝑥 − 6)(𝑥 + 1)
c) 𝑦 = 9𝑥^2 + 15𝑥 + 6
𝑦 = 3(3𝑥 + 2)(𝑥 + 1)
d) 𝑦 = 2𝑥^3 + 4𝑥^2 − 16𝑥
𝑦 = 2𝑥(𝑥 − 4)(𝑥 + 2)
e) 𝑦 = 25𝑥^2 − 16
𝑦 = (5𝑥 + 4)(5𝑥 − 4)
To write the equation 𝑦 = 6𝑥 + 42 in factored form, we need to start by finding the greatest common factor (GCF) of the terms 6𝑥 and 42. In this case, the GCF is 6.
So, we can factor out 6 from both terms:
𝑦 = 6(𝑥 + 7)
Therefore, the equation 𝑦 = 6𝑥 + 42 in factored form is 𝑦 = 6(𝑥 + 7).