B3. Let $p(x)=3 x^{3}-2 x^{2}-3$ and $q(x)=x+1$.

a) Calculate $3 p(-2)+2 q(3)$.

b) Write the leading term of the polynomial $2(p(x))^{2}$.

c) Calculate $p(x) \cdot(q(x))^{2}$.

d) Divide $p(x)$ by $q(x)$.
B3. The value of the expression $3 p(-2)+2 q(3)$ is calculated by substituting the chosen values into $p(x)$ and $q(x)$. We get -97. The leading term of the polynomial $2(p(x))^{2}$ is $18 x^{6}$. The product $p(x) \cdot q(x)$ is equal to $3 x^{5}+4 x^{4}-x^{3}-5 x^{2}-6 x-3$. By the fundamental theorem of division, we write $p(x)=$ $\left(3 x^{2}-5 x+5\right)(x+1)-8$.

Calculated value: $3 p(-2)+2 q(3)=-97 \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . \ldots$ point

![](https://cdn.mathpix.com/cropped/2024_06_07_4401d59a37898c9fd2b4g-16.jpg?height=57&width=1642&top_left_y=277&top_left_x=273)

Correctly calculated product $3 x^{5}+4 x^{4}-x^{3}-5 x^{2}-6 x-3 \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . \ldots$ points

Correctly performed division and result $p(x)=\left(3 x^{2}-5 x+5\right)(x+1)-8 \ldots \ldots \ldots .2$ points