Questions: Skills Review Homework Question 4, R.2.27 HW Score: 65%, 130 Points: 0 of 1 Factor the following polynomial. If a polynomial cannot be factored, write prime. Factor out the greatest common factor as necessary. 9 p^2 - 24 p + 16 Select the correct choice below and fill in any answer boxes within your choice. A. 9 p^2 - 24 p + 16 = (Type your answer in factored form.) B. The polynomial is prime.

Solution Steps

To factor the given polynomial \(9p^2 - 24p + 16\), we can use the method of factoring trinomials. Specifically, we look for two binomials \((ap + b)(cp + d)\) such that their product equals the given polynomial. We can also check if the polynomial is a perfect square trinomial.

1. Identify the coefficients: \(a = 9\), \(b = -24\), and \(c = 16\).
2. Check if the polynomial is a perfect square trinomial by verifying if it can be written as \((mp + n)^2\).
3. If it is a perfect square trinomial, factor it accordingly.
4. If it is not, use the quadratic formula to find the roots and then express the polynomial in its factored form.

We are given the polynomial: \[ 9p^2 - 24p + 16 \]

We need to determine if the polynomial can be written as a perfect square trinomial. A perfect square trinomial takes the form: \[ (ap + b)^2 \]

We factor the polynomial: \[ 9p^2 - 24p + 16 = (3p - 4)^2 \]

Since we successfully factored the polynomial, it is not prime.

Final Answer