Question

We are looking to factor 23x^2 + kx - 5. Some values of k allow us to factor it as a product of linear binomials with integer coefficients. What are all such values of k?

Answer 1

-115, -18, 18, 115

Explanation:

As 23 & 5 are prime numbers, so the probabilities are:

• (23x + 5)(x - 1) = 23x² - 18x -5 ⇒ k = -18
• (23x - 5)(x + 1) = 23x² + 18x -5 ⇒ k = 18
• (23x + 1)(x - 5) = 23x² - 115x -5 ⇒ k = -115
• (23x - 1)(x + 5) = 23x² + 115x -5 ⇒ k = 115

Answer 2

Explanation:

23 and 5 are prime numbers and are of opposite sign so k=±(23-5)=±18