Question

Match the trinomial with a correct factorization. A. \((x+5)(x-4)\) B. \((x+4)(x+5)\) c. \((x-4)(x-5)\) D. \((x+4)(x-5)\) $$x^{2}-x-20$$

Short answer

The correct factorization for the equation \(x^{2}-x-20\) is \((x+4)(x-5)\), hence the answer is option D.

Step-by-step solution

Analyze the Options

There are four options to choose from. Each option is a factored form of a quadratic equation. By expansion, each will result in a different quadratic equation. The goal is to find which one gives \(x^{2}-x-20\) when expanded.

Expand each option

Start from option A: Multiply \(x+5\) and \(x-4\) to get \(x^{2}+x-20\). This is not the required equation, so it's not the correct option. Option B: Multiply \(x+4\) and \(x+5\) to get \(x^{2}+9x+20\). This is not the required equation, so it's not the correct option. Option C: Multiply \(x-4\) and \(x-5\) to get \(x^{2}-9x+20\). This is not the required equation, so it's not the correct option. Option D: Multiply \(x+4\) and \(x-5\) to get \(x^{2}-x-20\). This is the required equation, so the answer is option D.