Question

1. which function is equivalent to ( h(x) = x^2 + 2x - 15 )?

• ( h(x) = (x + 3)(x - 5) )
• ( h(x) = (x + 5)(x - 3) )
• ( h(x) = (x + 1)(x - 15) )
• ( h(x) = (x + 15)(x - 1) )

clear all

Explanation:

Step1: Recall factoring quadratic

To factor \(x^2 + bx + c\), find two numbers that multiply to \(c\) and add to \(b\). Here, \(b = 2\), \(c=-15\). We need two numbers that multiply to \(-15\) and add to \(2\).

Step2: Find the numbers

The numbers \(5\) and \(-3\) work: \(5\times(-3)=-15\) and \(5 + (-3)=2\).

Step3: Factor the quadratic

So, \(x^2 + 2x - 15=(x + 5)(x - 3)\).

Answer:

\(k(x)=(x + 5)(x - 3)\) (the second option)