Equivalent Expressions
This expression is equivalent to
(2x)(x+3)(x-4).
2x3-2x2-24x
The standard form of a polynomial.
Terms arranged in descending order of their degree followed by the others.
Ex.2x2+3x+4
Ex. 5x4+3x3+2x+1
Write a possible equation for a polynomial whose graph has the following zeros:
-3, 0.
(x+3)(x)
or
(2x+6)(x)
The expression for the volume of an open-top box created by cutting squares of side length x from each corner of a 8-foot by 6.5-foot piece of cardboard and folding up the sides.
V(x)=(8-2x)(6.5-2x)(x)
The graph of f(x)=x2-4x+3 opens in this direction.
Upward
This expression is equivalent to
(x-2)(x+1)(x-3).
x3-4x2+x+6
The definition of a polynomial.
A function given by a sum of terms, each of which is a constant times a whole number power of x (or variable).
Write a possible equation for a polynomial whose graph has the following horizontal intercepts:
(-2, 0), (1/4, 0), (4, 0).
(x+2)(x-1/4)(x-4)
or
(2x+6)(4x-1)(x-4)
Given the function V(x)=(x)(10-2x)(8-2x)
Rewrite this function in standard form.
V(x)=4x3-36x2+80x
The y-intercept of the function f(x)=2x3-5x2+3x-7 is this point.
(0, -7)
This expression is equivalent to
(4x)(x+2)(x-1)(x+3).
4x4+16x3+4x2-24x
The definition of zeros.
The input values (x-values) that make the function's output (y-value) equal to zero.
Write a possible equation for a polynomial whose graph has the following zeros:
-1/2, 3, 5, and 7.
(x+1/2)(x-3)(x-5)(x-7)
or
(2x-1)(x-3)(x-5)(x-7)
Given the function V(x)=4x3-28x2+45x, where the side lengths of the square cutouts are x feet.
What is the volume of the box when x=2?
V(2)=4(2)3-28(2)2+45(2)
V(2)=32-112+90
V(2)=10ft3
The x-intercepts for the function f(x)=(x-4)(x+2)(2x-1).
(4, 0), (-2, 0), and (1/2, 0)
This expression is equivalent to
(-2x)(x-5)(x+1)(2x+3).
-4x4+10x3+44x2+30x
The definition of degree.
The largest exponent on a variable in a polynomial.
Select ALL the expressions that could represent the polynomial p, where the graph of p has zeros at -1, 1/3, and 5.
a. (x)(x+1)(x-5)
b. (x+1)(3x-1)(x-5)
c. (3x)(x-1)(x-1/3)(x-5)
d. (x+1)(x-1/3)(x-5)
b. (x+1)(3x-1)(x-5)
d. (x+1)(x-1/3)(x-5)
The expression for the volume of an open-top box created by cutting squares of side length x from each corner of a 12-inch by 10-inch piece of paper and folding up the sides.
The volume of the box when x=4.
V(x)=x(12-2x)(10-2x)
V(4)=4(12-8)(10-8)
V(4)=4(4)(2)
V(4)=32in3
These key features should be shown when graphing a polynomial function.
The x-intercepts (horizontal intercepts), y-intercept (vertical intercept), relative maximum, and relative minimum.
This expression is equivalent to
(5x)(x-1)(x+3)(x-2).
5x4-35x2+30x
The formula for volume.
V=lwh
Two expressions that could represent a polynomial with zeros at -2, 1/2, and 4.
(x + 2)(2x - 1)(x - 4) and (x + 2)(x - 1/2)(x - 4)
What is a math teacher’s favorite season?
SUMmer.
What shape is usually waiting for you inside a Starbucks?
A line.