Supply the missing term to make the given polynomials a perfect trinomial square then find the factors.
y2 – 8y + _____


To make the given polynomial a perfect square trinomial, we need to find the missing term that will allow it to be factored as the square of a binomial.

### Step 1: Identify the coefficient of the linear term
The given polynomial is:

\[
y^2 - 8y + \text{____}
\]

Here, the coefficient of the linear term (the \(y\) term) is \(-8\).

### Step 2: Find the missing term
To complete the square, take half of the coefficient of the linear term and then square it:

\[
\left(\frac{-8}{2}\right)^2 = (-4)^2 = 16
\]

So, the missing term is \(16\).

### Step 3: Write the complete perfect square trinomial
Now, the polynomial becomes:

\[
y^2 - 8y + 16
\]

### Step 4: Factor the trinomial
The trinomial can now be factored as:

\[
(y - 4)^2
\]

So, the missing term is \(16\), and the factors of the trinomial are \((y - 4)(y - 4)\) or \((y - 4)^2\).

Would you like further details or have any questions?

Here are 5 related questions to explore:
1. How do you complete the square for a trinomial with a different coefficient on the \(y^2\) term?
2. What if the linear term had been positive, how would that change the process?
3. Can you explain why the process of completing the square works for all quadratic equations?
4. What are other methods to factor a quadratic polynomial besides completing the square?
5. How do you solve a quadratic equation once it’s been factored?

**Tip:** When completing the square, always remember to adjust for the squared term's coefficient if it isn't 1.

Learn how to complete the square to find the missing term in the quadratic polynomial y^2 - 8y + ____. Explore the process step-by-step and understand how to factor the resulting perfect square trinomial. Suitable for high school students studying quadratic equations and algebraic factorization.

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