Lesson 4
Combining Polynomials
- Let's do arithmetic with polynomials.
Problem 1
Here are two expressions whose product is a new expression, A.
\displaystyle (5x^4 + \boxed{\phantom{33}}x^3)(4x^{\boxed{\phantom{3}}} - 6) = A
Andre says that any real number can go in either of the boxes and A will be a polynomial. Is he correct? Explain your reasoning.
Problem 2
Lin divides the polynomial 2x^2 - 4x + 1 by 4 and gets 0.5x^2 - x + 0.25. Is 0.5x^2 - x + 0.25 a polynomial? Explain your thinking.
Problem 3
What is the result when any 2 integers are multiplied?
a positive integer
a negative integer
an integer
an even number
Problem 4
Clare wants to make an open-top box by cutting out corners of a 30 inch by 25 inch piece of poster board and then folding up the sides. The volume V(x) in cubic inches of the open-top box is a function of the side length x in inches of the square cutouts.
- Write an expression for V(x).
- What is a reasonable domain for V in this context?
Problem 5
Identify the degree, leading coefficient, and constant value of each of the following polynomials.
- f(x)=2x^5 - 8 x^2 - x - 6
- h(x)=x^3 - 7 x^2 - x + 2
- g(x)=5 x^2-4 x^3 + 2x +5.4
Problem 6
Which point is a relative minimum?
A
B
C
D