Polynomial Basics
Define a polynomial
What is an expression made up of terms with variables raised to whole number exponents and real coefficients?
Factors of x2-9
What are (x-3) and (x+3)
End behaviour of x3
Solutions of x2=16
What are 4 and -4?
Dimensions of a square with an area of x2+5x+6
What are (x+3) and (x+2)?
Degree of 4x5-2x3+7
What is 5?
What are (x+2) and (x+3)
Sketch of y=x2(x-1)
Degree 3, opens up, x-intercept at 0 (order 2), x-intercept at 1 (order 1)
Solutions of x2+3x=0
What are 0 and -3?
Maximum profit for P(x)=-2x2+12x-16
What is maximum profit when x=3, P(3)=2?
Leading coefficient of x2-3x4
What is -3?
What are (2x) and (x-4)
What are 1 or 3 turning points and 1, 2 or 3 x-intercepts?
Solutions of x3-x=0?
What are 0, 1, and -1?
Meaning of x-intercepts for a profit function
Breakeven points - when profit = 0 (expenses = revenue)
No, because 1/x has a negative exponent (-1), which is not a whole number.
Factors of x3+3x2-4x-12
What are (x+3) (x-2) and (x+2)?
What is point symmetry?
Solutions of x4-5x2+4.
What are 1, -1, 2, and -2?
Max height of bridge following the path of -x2+6x
What is a vertex at (3, 9)?
The difference between a polynomial function and a power function
Power functions have a single term with a real coefficient and a variable raised to a whole number.
Polynomial functions have multiple terms, each with a real coefficient and a variable raised to a whole number.
Factors of x4-1
What are (x-1) (x+1) and (x2+1)?
Graph of x3-3x2-6x+8
What are x-intercepts at x = -2, 1, 4, opening up.
Solutions of x3+x2-x-1=0.
What are -1 and 1?
Breakeven points of the cost function C(x)=x3-6x2+11x-6
What are x = 1, 2, and 3?