Questions: Factor the following trinomial: y^2 - 7y - 18

Transcript text: Question Factor the following trinomial: $y^{2}-7 y-18$ Provide your answer below:

Solution

Solution Steps

To factor the trinomial $ y^2 - 7y - 18 $, we need to find two numbers that multiply to the constant term (-18) and add up to the coefficient of the linear term (-7). Once we find these numbers, we can rewrite the middle term and factor by grouping.

Step 1: Identify the Trinomial

We start with the trinomial: \[ y^2 - 7y - 18 \]

Step 2: Find Two Numbers

We need to find two numbers that multiply to $-18$ (the constant term) and add up to $-7$ (the coefficient of the linear term).

Step 3: Factor the Trinomial

The two numbers that satisfy these conditions are $-9$ and $2$. Therefore, we can rewrite the trinomial as: \[ y^2 - 9y + 2y - 18 \]

Step 4: Group and Factor by Grouping

Group the terms to factor by grouping: \[ (y^2 - 9y) + (2y - 18) \]

Factor out the common factors in each group: \[ y(y - 9) + 2(y - 9) \]

Step 5: Factor Out the Common Binomial

Factor out the common binomial $(y - 9)$: \[ (y - 9)(y + 2) \]

Final Answer

The factored form of the trinomial $ y^2 - 7y - 18 $ is: \[ \boxed{(y - 9)(y + 2)} \]

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