For Mathguru
1
Polynomial Functions Assignment Name: ________________________
1. Which of the following is NOT a polynomial function? Explain. (1 mark)
a. 4 23 0.5 2y x x x
b. 23 2 xy
x
c. 2 2
2
3
2 2
x xy
d. 2
2 2y x x
2. If k, 3k, and -3k/2 are zeros of 3665)( 23
kxxxxP , and k > 0, find k and write the
factored form of the polynomial. (1 mark)
3. When a certain polynomial is divided by 2x , the quotient is 2
4 1x x and the remainder
is 8. What is the polynomial? (1 mark)
4. Sketch the graph given the following information: (1 mark)
Degree: 3
Zeros: -2, 1
Leading Coefficient : negative
y-int: 4
2
5. Given the polynomial function 22)( 43 xxxxP with x-intercept = -3,
(4 marks)
• Determine the quotient and remainder using long division. Write the Polynomial
Statement: ax
R xQ
ax
xP
)(
)( .
• Determine the quotient and remainder using synthetic division and state the restrictions on the variable.
3
6. The graph of a polynomial function, ( )P x , is shown below. (2 marks)
Write the equation of the polynomial, with lowest possible multiplicity.
7. Write a cubic function with x-intercepts of 3 ,
3 and 1 and a y-intercept of -1. (2
marks)
8. Determine the value(s) of k so that the binomial is a factor of the polynomial. (1 mark)
𝑥3 − 6𝑥2 + 𝑘𝑥 − 6, 𝑥 − 2
9. Factor the following Polynomial Function fully: (3 marks)
3648510112)(
423 xxxxxP
4
10. Quinn, Ralph and Audrey share a birthday on July 3. Quinn and Ralph are the same age, but
Audrey is two years older than either of the boys. The product of their ages is 11548 greater
than the sum of their ages. (2 marks)
a) Write a polynomial equation that can be used to find the age of each person.
b) Solve graphically the polynomial equation from part a). How old is each person?
11. A rectangular prism has a volume of 2100 3
cm . If the height of the prism is x cm and the
width and length of the base is 25x cm , and 10x +1 cm, respectively, find the dimensions of
the rectangular prism. Solve algebraically.
(2 marks)