## Final Answer

## Step-by-step Solution

Problem to solve:

Solving method

We can multiply the polynomials $\left(x+1\right)\left(x-4\right)$ by using the FOIL method. The acronym F O I L stands for multiplying the terms in each bracket in the following order: First by First ($F\times F$), Outer by Outer ($O\times O$), Inner by Inner ($I\times I$), Last by Last ($L\times L$):

- ($F\times F$) is $(x)(x)$
- ($O\times O$) is $(x)(-4)$
- ($I\times I$) is $(1)(x)$
- ($L\times L$) is $(1)(-4)$

Then, combine the four terms in a sum: $(F\times F) + (O\times O) + (I\times I) + (L\times L)$:

Multiply $1$ times $-4$

Any expression multiplied by $1$ is equal to itself

When multiplying two powers that have the same base ($x$), you can add the exponents

Combining like terms $-4x$ and $x$