Question

Rybinsky’s Apparels profit can be modeled by the function, p(x)=3x² − 17x + 10. The zeros of Rybinsky's Apparels profit function are 5 and 23. If one of the factors of the profit function is (x−5), which expression below could be the second factor?

Answer 1

The second factor of the profit function must be (x−5)(3x−2).

Let's factor the expression:

3x^2 −17x+10

We will use the sum-product pattern and factoring by grouping to solve this problem.

Steps to solve:

1. Use the sum-product pattern:

3x^2 −2x−15x+10

2. Extract the common factors:

x(3x−2)−5(3x−2)

3. Rewrite in factored form:

(x−5)(3x−2)

Answer:

(x−5)(3x−2)