Question

Fill in the blanks to complete the examples.
Rules for Factoring ax? + bx + c
Rules in Words
Variables
Example
Any reducible trinomial can be ax?+bx +c= factored as (rx + p)(sx + q).
(rx+ p)(sx +q)
6x2+13x+5
=
(3x + 5)(2x+
The product of r and s is the leading coefficient, a.
ros=
Answer
Answer
=6
The product of p and q is the constant term, c.
p•q=
• Answer
Answer
=5

Options:
5 • 1
3 • 2
a
c

Answer 1

Let's fill in the blanks with the relevant information and use the options provided:

1. **Any reducible trinomial can be ax² + bx + c = factored as (rx + p)(sx + q).**
- **Variables**: (rx + p)(sx + q)
- **Example**: 6x² + 13x + 5 = (3x + 5)(2x + 1)

2. **The product of r and s is the leading coefficient, a.**
- **ros = 6**

3. **The product of p and q is the constant term, c.**
- **p • q = 5**

So, filling in the blanks with the specific numbers:
- r = 3, s = 2, p = 5, q = 1.

Thus, we have:
- The factoring of 6x² + 13x + 5 results in (3x + 5)(2x + 1).
- The product of the coefficients leading to a = 6, and the product of the constants leading to c = 5.