Let f(x)=2x^2+3 and g(x)=−x^2+6x+2. Which statements below are true for f(x)⋅g(x)? Select all that apply.
A. The resulting polynomial has degree 4
B. The x^2 term has a coefficient of −1
C. The constant term is 6
D. The leading term is 2x^4
E. The x^3 term has a coefficient of 12
F. The x has a coefficient of 1
f(x)⋅g(x) = (2x^2 + 3)(-x^2 + 6x + 2)
= -2x^4 + 12x^3 + 4x^2 - 3x^2 + 18x + 6
= -2x^4 + 12x^3 + x^2 + 18x + 6
Therefore, the correct statements are:
A. The resulting polynomial has degree 4
D. The leading term is 2x^4
are u sure
Apologies for the error in my previous response. Let's correct it:
f(x) = 2x^2 + 3 and g(x) = -x^2 + 6x + 2
f(x) ⋅ g(x) = (2x^2 + 3) ⋅ (-x^2 + 6x + 2)
= -2x^4 + 12x^3 + 4x^2 - 3x^2 + 18x + 6
= -2x^4 + 12x^3 + x^2 + 18x + 6
From the above expression, the correct statements are:
A. The resulting polynomial has degree 4 because of the term -2x^4.
B. The x^2 term has a coefficient of 1.
C. The constant term is 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.
A. Length: L(s)=2y Width: W(s)=y+2
B. Length: L(s)=2+y Width: W(s)=2y
C. Length: L(s)=y^2 Width: W(s)=2y
D. Length: L(s)=y^2 Width: W(s)=y+2
Length of rectangle = 2y (twice the side length of the square)
Width of rectangle = y + 2 (2 units longer than the side length of the square)
So, the correct expressions are:
A. 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.
A. A(s)=6y+4
B. A(s)=3y+2
C. A(s)=2y^2+4
D. A(s)=2y^3+2y^2
E. A(s)= 2y^2+4y
The area of a rectangle is given by length multiplied by width.
Area of rectangle = L(s) * W(s)
Area of rectangle = (2y) * (y + 2)
Area of rectangle = 2y^2 + 4y
The function to represent the area of the rectangle in terms of the sides of the square is:
E. A(s) = 2y^2 + 4y