Polynomial Word Problems

Solving Word Problems Involving Polynomial Functions

by Marcel Hilotin

​Let's Recall Polynomials

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Multiple Choice

What is the y-intercept of the polynomial $$y=\left(x-1\right)\left(x-2\right)\left(x+3\right)$$  

• 1

• 2

• -3

• 6

Multiple Choice

Smooth and Continuous looks like

Multiple Choice

$$6a^2x^2+15a^2x$$  can be written in factored form as

• $$\left(ax\right)\left(6ax+15a\right)$$

• $$\left(3x\right)\left(2ax+5a\right)$$

• $$\left(3a^2x\right)\left(2x+5\right)$$  

• prime

Multiple Choice

Which of the following is a polynomial?

• $$2x^4-3\sqrt[]{x^3}+x-1$$  

• $$5x^3-\frac{1}{x^2}+x$$  

• $$3x^3+2x^2-x^{-1}+4$$  

• $$4x^3-2x+5$$  

Multiple Choice

$$x^2+3x-4x^3$$   written in standard form

• $$4x^3+x^2+3x$$  

• $$x^2+3x-4x^3$$  

• $$3x+x^2-4x^3$$  

Multiple Choice

Determine the end behaviors of the graph

• Rising to both left and right

• Falling to both left and right

• Rises to the left and falls to the right

• Falls to the left and rises to the right

​Solving Problems...

​A rectangular box is 24 in. long, 12 in. wide, and 18 in. high. If each dimension is increased by x in., write a polynomial function in standard form modeling the volume V of the box.

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Multiple Select

Which should be used to determine the end behaviors of the graph?

• degree of the polynomial

• constant term

• the number of terms

• sign of the leading coefficient