Is this composition of polynomial correct? Suppose $p(x)=x^2+5x+3$ and $q(x)=3x^3-3x+7$. Write the expression $(q \circ p)(x)$ as a sum of terms, each which is a constant times the power of $x$.
Here is my work for the problem:
$(q\circ p)(x)=3(x^2+5x+3)^3-3(x^2+5x+3)+7$
$(q\circ p)(x)=3(x^6+125x^3+27)-3x^2-15x-9+7$
$(q\circ p)(x)=3x^6+375x^3+81-3x^2-15x-2$
$(q\circ p)(x)=3x^6+375x^3-3x^2-15x+79$
Did I do something wrong while working with this problem? The final answer I got wasn't in the multiple choice answers. I went over this problem 3 times and cannot find what I am doing wrong.

As Jasper noted you did wrong here: $$...=3(x^2+5x+3)^3...$$ $$...=3(x^6+125x^3+27)-...$$ In fact $$(a+b+c)^3=a^3 + 3a^2b + 3a^2c + 3ab^2 + 6abc + 3ac^2 + b^3 + 3b^2c + 3bc^2 + c^3$$ we have $q(p(x))=3x^6+45x^5+252x^4+645x^3+753x^2+390x+79$
