Question

consider the trinomial $6x^2 + 13x + 6$. the value of $ac$ is \boxed{\quad}. the value of $b$ is \boxed{\quad}. the two numbers that have a product of $ac$ and a sum of $b$ are 4 and \boxed{\quad}.

Explanation:

Step1: Calculate $ac$

For $6x^2+13x+6$, $a=6$, $c=6$.
$ac = 6 \times 6 = 36$

Step2: Identify value of $b$

From the trinomial, $b$ is the coefficient of $x$.
$b = 13$

Step3: Find missing sum number

Let the missing number be $n$. We know $4 + n = 13$.
$n = 13 - 4 = 9$
Verify product: $4 \times 9 = 36 = ac$, which matches.

Answer:

The value of $ac$ is 36.
The value of $b$ is 13.
The two numbers that have a product of $ac$ and a sum of $b$ are 4 and 9.