Questions: Completely factor the trinomial, if possible. x^2-3x-10

Transcript text: Completely factor the trinomial, if possible. \[ x^{2}-3 x-10 \]

Solution

Solution Steps

To factor the trinomial \(x^2 - 3x - 10\), we need to find two numbers that multiply to the constant term (-10) and add up to the linear coefficient (-3). Once these numbers are identified, we can express the trinomial as a product of two binomials.

Step 1: Identify the Trinomial

We start with the trinomial \(x^2 - 3x - 10\). Our goal is to factor this expression into the form \((x + a)(x + b)\), where \(a\) and \(b\) are numbers that we need to determine.

Step 2: Find the Factors

We need to find two numbers that multiply to the constant term \(-10\) and add up to the linear coefficient \(-3\). The numbers that satisfy these conditions are \(-5\) and \(2\) because: \[ -5 \times 2 = -10 \quad \text{and} \quad -5 + 2 = -3 \]

Step 3: Write the Factored Form

Using the numbers found, we can express the trinomial in its factored form: \[ x^2 - 3x - 10 = (x - 5)(x + 2) \]