Question

factor trinomials (a=1)
score: 0/3 penalty: 0.25 off
question
watch video
factor.
$x^2 + 17x + 72$

Explanation:

Step1: Find two numbers that multiply to 72 and add to 17.

We need to find two integers \( m \) and \( n \) such that \( m \times n = 72 \) and \( m + n = 17 \).
The factor pairs of 72 are: (1, 72), (2, 36), (3, 24), (4, 18), (6, 12), (8, 9).
Checking the sums: \( 8 + 9 = 17 \).

Step2: Factor the trinomial.

For a trinomial \( x^2 + bx + c \) (where \( a = 1 \)), we can factor it as \( (x + m)(x + n) \) where \( m \) and \( n \) are the numbers found in Step 1.
So, \( x^2 + 17x + 72 = (x + 8)(x + 9) \).

Answer:

\( (x + 8)(x + 9) \)