Question

factor the trinomial.
(a^2 - ay - 30y^2)
(a^2 - ay - 30y^2 = square)

Explanation:

Step1: Identify the form

We have a trinomial \( a^2 - ay - 30y^2 \). We need to factor it in the form \( (a + my)(a + ny) \), where \( m\times n=- 30 \) and \( m + n=-1 \).

Step2: Find m and n

We need two numbers \( m \) and \( n \) such that their product is \(-30\) and their sum is \(- 1\). Let's list the factor pairs of \(-30\):

• \( ( - 6)\times5=-30 \) and \( - 6 + 5=-1 \)

Step3: Factor the trinomial

Using the values of \( m=-6 \) and \( n = 5 \), we can factor the trinomial as:
\( a^2-ay - 30y^2=(a-6y)(a + 5y) \)

Answer:

\((a - 6y)(a + 5y)\)