1. When the expression $4(x^2-2x+2)-7(x^3-3x+1)$ is fully simplified, what is the sum of the squares of the coefficients of the terms?
2. If $p(t)$ and $q(t)$ are both seventh-degree polynomials in $t$, what is the degree of $p(t)\cdot q(t)$?
3. Define the function $g(x)=3x+2$. If $g(x)=2f^{-1}(x)$ and $f^{-1}(x)$ is the inverse of the function $f(x)=ax+b$, find $\dfrac{a+b}{2}$.
+118608 1. When the expression $4(x^2-2x+2)-7(x^3-3x+1)$ is fully simplified, what is the sum of the squares of the coefficients of the terms?
\(4(x^2-2x+2)-7(x^3-3x+1)\\ =4x^2-8x+8\;\;-7x^3+21x-7\\ =-7x^3+4x^2+13x+1\\ \text{The coefficients of the terms are -7, 4, 13 }\\ \text{The squares of the coefficients of the terms are 49, 16, 169 }\\ \text{The sum of the squares is }49+16+169 \)
49+16+169 = 234
+118608 2. If $p(t)$ and $q(t)$ are both seventh-degree polynomials in $t$, what is the degree of $p(t)\cdot q(t)$?
the leading terms will be ax^7 and bx^7 Where a and b are real numbers
When these are multiplied together they will give abx^14
So the degree of p(t)\cdot q(t) will be 14
