Polynomial Functions Practice Problems

Here you will find a concise collection of polynomial functions practice problems. Visit this page directly at hunkim.com/polynomials

1. f(x)=(x+1)(x+2)(x-2)
   1. What are the roots of this polynomial function?
   2. Find the y-intercept
   3. Expand this polynomial function to the form y=ax^3+bx^2+cx+d
      
2. True or False: x^2+(x+4)^{0.5} is a polynomial
   
3. True or False: -\sqrt{2}\pi x^3-4 is a polynomial
   
4. Sketch an odd degree polynomial with a y-intercept of -5 with a root of 2.
   
5. What is the range of possible x-intercepts given: f(x)=ax^5+bx^4+cx^3+dx^2+ex+f?
   
6. What is the range of possible x-intercepts given: g(x)=ax^4+bx^3+cx^2+dx+e?
   
7. What is the remainder when x^4-8x^2+9x+8 is divded by x+6?
   
8. Factor x^3+2x^2-4x-8
   
9. Determine the value of k so that x+2 is a factor of x^3+10x^2+23x+k
   
10. What are the roots of the graph below?
    
    
11. (x-2) is a factor of P(x)=x^3+4x^2-3x-18. Factor P(x) fully.
    
12. \frac{x^3+3x^2-7}{x+2}=x^2+x-2+A. Find A
    
13. Sketch y=-(x+3)^3(x-1)^2(x). Clearly label the roots, and show the behavior of the graph’s multiplicities.
    
14. Factor x^3-8
    
15. Factor 8a^3+b^3