+0  
 
0
147
2
avatar

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
avatar+92873 
+2

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
 #2
avatar+92873 
+2

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

8 Online Users

avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.