5)
Let f(x)=2x2+3
and g(x)=−x2+6x+2
. Which statements below are true for f(x)⋅g(x)
? Select all that apply.
(3 points)
Responses
The resulting polynomial has degree 4
The resulting polynomial has degree 4
The x
has a coefficient of 1
The x has a coefficient of 1
The constant term is 6
The constant term is 6
The leading term is 2x4
The leading term is 2 x to the 4th power
The x3
term has a coefficient of 12
The x cubed term has a coefficient of 12
The x2
term has a coefficient of −1
The resulting polynomial has degree 4: False (The resulting polynomial has degree 2)
The x has a coefficient of 1: False (The coefficient of x is different in each term)
The constant term is 6: False (The constant term is 3, not 6)
The leading term is 2x^4: False (The leading term is 2x^2, not 2x^4)
The x^3 term has a coefficient of 12: False (There is no x^3 term in the resulting polynomial)
The x^2 term has a coefficient of -1: False (The coefficient of x^2 is 2, not -1)
6)
The sides of a square all have a side length of y
. Write a simplified area function in terms of y
for a rectangle whose length is twice the side length of the square and whose width is 2 units longer than the side length of the square.
Part A: Express both the length and the width of the rectangle as a function of a side of the square.
(1 point)
Responses
Length: L(s)=2y
Width: W(s)=y+2
Length: cap l times s is equal to 2 y Width: cap w times s is equal to y plus 2
Length: L(s)=2+y
Width: W(s)=2y
Length: cap l times s is equal to 2 plus y Width: cap w times s is equal to 2 y
Length: L(s)=y2
Width: W(s)=2y
Length: cap l times s is equal to y squared Width: cap w times s is equal to 2 y
Length: L(s)=y2
Width: W(s)=y+2
Length: L(s)=2y
Width: W(s)=y+2
Part B: Write a function to represent the area of the rectangle in terms of the sides of the square. (1 point)
Responses
A(s)=2y2+4
cap A times s is equal to 2 y squared plus 4
A(s)=2y3+2y2
cap A times s is equal to 2 y cubed plus 2 y squared
A(s)= 2y2+4y
A(s)= 2y2+4y
A(s)=3y+2
cap A times s is equal to 3 y plus 2
A(s)=6y+4