The polynomial expressions 3y^3+39y^2+90y and y^2-7y-30 share a common binomial factor. What binomial factor do they share?

y + 3

Step-by-step explanation:

Let P₁ = 3y³ + 39y² + 90y

and P₂ = y² - 7y - 30

Factor P₁

P₁ = 3y³ + 39y² + 90y

Remove the common factor 3y

P₁ = 3y (y² + 13y + 30)

Factor the quadratic

P₁ = 3y (y + 3) (y + 10)

Factor P₂

P₂ = y² - 7y - 30

P₂ = (y + 3) (y - 10)

The common binomial factor of P₁ and P₂ is y + 3.