Question

factor the trinomial completely.

\\p^2 - 12p + 27\\

select the correct choice below and fill in any answer boxes within your choice.

a. \\p^2 - 12p + 27 = \\

b. the polynomial is prime.

Explanation:

⚡ Using what you learned: factoring trinomials

Step 1: Identify the coefficients

Identify the values of \( a \), \( b \), and \( c \) in the quadratic expression \( ap^2 + bp + c \):

$$ a = 1, \quad b = -12, \quad c = 27 $$

Step 2: Find factors of \( c \) that add up to \( b \)

Find two numbers that multiply to \( 27 \) and add up to \( -12 \):

$$ (-3) \cdot (-9) = 27 $$

$$ (-3) + (-9) = -12 $$

Step 3: Write the factored form

Use the factors \( -3 \) and \( -9 \) to write the binomial factors:

$$ (p - 3)(p - 9) $$

Answer:

A. \( p^2 - 12p + 27 = (p - 3)(p - 9) \)