The differnce of R(x) and C(x) is [tex]=x^{4} -3x^{3}+x^{2}-4[/tex]. Therefore, option D is the correct answer.
Given that, [tex]R(x)=2x^{4} -3x^{3} +2x-1[/tex] and [tex]C(x)=x^{4} -x^{2} +2x+3[/tex].
We need to find the value of P(x)=R(x)-C(x).
How to subtract the algebraic expression?
To subtract an algebraic expression from another, we should change the signs (from '+' to '-' or from '-' to '+') of all the terms of the expression which is to be subtracted and then the two expressions are added.
Now, R(x)-C(x)=[tex]2x^{4} -3x^{3} +2x-1-(x^{4} -x^{2} +2x+3)[/tex]
[tex]=2x^{4} -3x^{3} +2x-1-x^{4}+x^{2} -2x-3[/tex]
P(x)[tex]=x^{4} -3x^{3}+x^{2}-4[/tex]
Therefore, option D is the correct answer.
To learn more about the subtraction of expression visit:
https://brainly.com/question/12959016.
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