Questions: Factor the following trinomial. If it cannot be factored, indicate "Not Factorable". x^2+3x-4

Transcript text: Factor the following trinomial. If it cannot be factored, indicate "Not Factorable". \[ x^{2}+3 x-4 \]

Solution

Solution Steps

To factor the trinomial \(x^2 + 3x - 4\), we need to find two numbers that multiply to the constant term (-4) and add up to the linear coefficient (3). If such numbers exist, the trinomial can be factored into two binomials. If not, it is not factorable.

Step 1: Identify the Trinomial

We start with the trinomial \(x^2 + 3x - 4\).

Step 2: Factor the Trinomial

To factor the trinomial, we look for two numbers that multiply to \(-4\) (the constant term) and add up to \(3\) (the coefficient of \(x\)). The numbers \(4\) and \(-1\) satisfy these conditions since: \[ 4 \cdot (-1) = -4 \quad \text{and} \quad 4 + (-1) = 3 \]

Step 3: Write the Factored Form

Using the identified numbers, we can express the trinomial in its factored form: \[ x^2 + 3x - 4 = (x - 1)(x + 4) \]