Question

select the correct answer.

which binomial is a factor of the quadratic trinomial (x^2 - 7x + 12)?

(x + 2)
(x + 3)
(x - 4)
(x - 6)

Explanation:

⚡ Using what you learned: factoring trinomials

Step 1: Identify the coefficients

Identify the values of \( a \), \( b \), and \( c \) in the quadratic trinomial \( x^2 - 7x + 12 \):

$$ a = 1, \quad b = -7, \quad c = 12 $$

Step 2: Find two numbers that multiply to \( c \) and add to \( b \)

Find two integers whose product is \( 12 \) and whose sum is \( -7 \):

$$ -3 \times -4 = 12 $$

$$ -3 + (-4) = -7 $$

Step 3: Write the factored form

Write the trinomial as a product of two binomials:

$$ x^2 - 7x + 12 = (x - 3)(x - 4) $$

Step 4: Compare with the given options

The factors are \( (x - 3) \) and \( (x - 4) \). Comparing with the choices:

• \( (x + 2) \)
• \( (x + 3) \)
• \( (x - 4) \)
• \( (x - 6) \)

The binomial \( (x - 4) \) is a factor.

Answer:

\( (x - 4) \)