Given:
is subtracted from 3.
To find:
The result of the given statement in the standard form of the polynomial.
Solution:
We need to find the result when
is subtracted from 3.
So, the resulted polynomial can be written as:

On simplification, we get
![[\because (a+b)^2=a^2+2ab+b^2]](https://tex.z-dn.net/?f=%5B%5Cbecause%20%28a%2Bb%29%5E2%3Da%5E2%2B2ab%2Bb%5E2%5D)
Therefore, the resulted polynomial in standard form is
.
When shifted to the right 1 unit it would be:
f(x - 1) = (x - 1)^3 + 2(x - 1)^2 - 3(x - 1) - 5
<span>= (x^3 - 3x^2 + 3x - 1) + 2(x^2 - 2x + 1) - 3(x - 1) - 5 </span>
<span>= x^3 - 3x^2 + 2x^2 + 3x - 4x - 3x - 1 + 2 + 3 - 5 </span>
<span>= x^3 - x^2 - 4x - 1
</span>I hope this helps