Question

1. what are the factors of $x^2 + 7x + 12$?

a) $(x + 2)(x + 6)$
b) $(x + 4)(x + 3)$
c) $(x + 7)(x + 5)$
d) $(x + 12)(x + 1)$

Explanation:

Step1: Identify target sum and product

We need two numbers that add to $7$ (coefficient of $x$) and multiply to $12$ (constant term).

Step2: Find the pair of numbers

The numbers $3$ and $4$ satisfy: $3+4=7$ and $3\times4=12$.

Step3: Write the factored form

Substitute the numbers into the binomial factors: $(x+3)(x+4)$ (order does not matter).

Step4: Match with options

This matches option B.

Answer:

B) $(x + 4)(x + 3)$