Select the factored form of this expression. \[ x^{2}-3 x-28 \]

Below is a step-by-step solution to factor the quadratic expression. ### Step 1: Write Down the Expression We start with the quadratic expression: \[ x^{2} - 3x - 28 \] ### Step 2: Identify Two Numbers We need to find two numbers \( a \) and \( b \) such that: - Their product is equal to the constant term: \[ a \times b = -28 \] - Their sum is equal to the coefficient of \( x \): \[ a + b = -3 \] ### Step 3: Find the Pair that Works Consider the pair \( 4 \) and \( -7 \): - Product: \[ 4 \times (-7) = -28 \] - Sum: \[ 4 + (-7) = -3 \] The pair \( (4, -7) \) satisfies both conditions. ### Step 4: Write the Factored Form Using the numbers found, the expression can be factored as: \[ (x + 4)(x - 7) \] ### Final Answer The factored form of the expression \( x^{2} - 3x - 28 \) is: \[ \boxed{(x+4)(x-7)} \]