Questions: A. y^2 + 10y - 36 = (Factor completely.) B. The trinomial is prime.

Transcript text: A. $y^{2}+10 y-36=\square$ (Factor completely.) B. The trinomial is prime.

Solution

Solution Steps

To factor the trinomial $ y^2 + 10y - 36 $, we need to find two numbers that multiply to the constant term (-36) and add up to the coefficient of the linear term (10). If such numbers exist, we can factor the trinomial into two binomials. If not, the trinomial is prime.

Step 1: Identify the Trinomial

We are given the trinomial $ y^2 + 10y - 36 $.

Step 2: Attempt to Factor the Trinomial

To factor the trinomial, we look for two numbers that multiply to the constant term $-36$ and add up to the coefficient of the linear term $10$.

Step 3: Analyze the Factorization

After analyzing the possible pairs of factors of $-36$, we find that there are no two integers that satisfy both conditions. Therefore, the trinomial cannot be factored into simpler binomials.

Final Answer

The trinomial is prime. Thus, we conclude that:

$\boxed{\text{The trinomial is prime.}}$

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