Question

what value of g makes the equation true?
(x + 7)(x - 4) = x² + gx - 28

Explanation:

Step1: Expand the left - hand side

We use the distributive property (FOIL method) to expand \((x + 7)(x-4)\).
The FOIL method states that \((a + b)(c + d)=ac+ad+bc+bd\).
For \((x + 7)(x - 4)\), we have:
\(x\times x+x\times(-4)+7\times x + 7\times(-4)=x^{2}-4x + 7x-28\)

Step2: Combine like terms

Combine the \(x\) - terms: \(-4x+7x = 3x\).
So, \((x + 7)(x - 4)=x^{2}+3x-28\).

Step3: Compare with the right - hand side

We are given that \((x + 7)(x - 4)=x^{2}+gx-28\).
Comparing \(x^{2}+3x-28\) with \(x^{2}+gx-28\), we can see that the coefficient of \(x\) on the left - hand side is \(3\) and on the right - hand side is \(g\). So, \(g = 3\).

Answer:

\(3\)