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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 $\dfrac{a+b}{2}$.

Guest Mar 31, 2018
#1
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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

Melody  Mar 31, 2018
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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

Melody  Mar 31, 2018