Final answer:
The constant term needed to make the expression v² - 6v + ? a perfect square is 9, resulting in the perfect square trinomial v² - 6v + 9, which factors to (v - 3)².
Step-by-step explanation:
To fill in the blank and make the expression v² - 6v + ? a perfect square, we need to determine the constant term that completes the square. For a quadratic in the form v² + bv + c, we would complete the square by adding ²/4. Here, b is -6, so we compute (-6/2)² which equals 9. Therefore, the constant term c that completes the square is 9, making the expression a perfect square trinomial v² - 6v + 9, which factors into (v - 3)².
To make the expression v² - 6v + ? a perfect square, we need to find the value that completes the square. To do this, we take half of the coefficient of v and square it. In this case, we take half of -6, which is -3, and square it, which gives us 9. Therefore, the missing value is 9.