﻿ Polynomial Worksheets | Problems & Solutions

# Polynomial Worksheets

Polynomial Worksheets
• Page 1
1.
Determine the possible rational roots of 2$x$3 - $x$2 + 28$x$ + 5 = 0.
 a. ±1, ±$\frac{1}{2,}$ ±5 b. ±1, ±2, ±5 c. ±1, ±$\frac{1}{2,}$ ±$\frac{5}{2}$ ±5, d. ±$\frac{1}{2,}$ ±$\frac{5}{2}$ ±5,

2.
List out the possible rational roots of the polynomial 5$x$4 + 37$x$3 - 42$x$2 + 5$x$ + 7 = 0.
 a. ±1, ±7, ±$\frac{1}{7}$, ±$\frac{5}{7}$ b. ±1, ±$\frac{1}{7}$, ±$\frac{5}{7}$ c. ±1, ±7, ±$\frac{1}{5}$, ±$\frac{7}{5}$ d. ±1, ±5, ±$\frac{5}{7}$, ±$\frac{1}{7}$

3.
List all the possible rational roots of 4$x$5 + 7$x$4 - 2$x$2 + 5 = 0.
 a. ±1, ±2, ±4, ±5 b. ±1, ±2, ±4, ±$\frac{2}{5}$, ±$\frac{4}{5}$ c. ±1, ±5, ±$\frac{1}{2}$, ±$\frac{5}{2}$, ±$\frac{1}{4}$, ±$\frac{5}{4}$ d. ±1, ±$\frac{4}{5}$, ±$\frac{1}{2}$, ±$\frac{5}{2}$, ±$\frac{1}{4}$, ±$\frac{5}{4}$

4.
Determine the possible rational roots of the polynomial $x$3 - 3$x$2 + 2$x$ - 3 = 0.
 a. ±3, ±$\frac{1}{3}$ b. ±1. ±$\frac{1}{3}$ c. ±1, ±3 d. ±1, ±3, ±$\frac{1}{3}$

5.
If the product of three binomials is $x$3 + 3$x$2 - 10$x$ - 24. If one is $x$ + 2, what are the other two binomials?
 a. ($x$ - 3), ($x$ - 4) b. ($x$ + 3), ($x$ - 4) c. ($x$ - 3), ($x$ + 4) d. ($x$ + 3), ($x$ + 4)

6.
$x$ - 2 and $x$ - 4 are factors of $x$4 - 2$x$3 - 13$x$2 + 14$x$ + 24. Find the other factors.
 a. ($x$ + 1), ($x$ + 3) b. ($x$ - 1), ($x$ - 3) c. ($x$ + 1), ($x$ - 3) d. ($x$ - 1), ($x$ + 3)

7.
The volume of a box is given by the expression (125$x$3 - 150$x$2 + 55$x$ - 6) cm3. Its height is (5$x$ - 2) cm. What expressions are used to represent the other two dimensions?
 a. (5$x$ - 2) and (5$x$ - 3) b. (5$x$ - 1) and (5$x$ - 2) c. (5$x$ - 1) and (5$x$ - 3) d. (5$x$ + 1) and (5$x$ + 3)

8.
Tim expresses the product of four numbers as $x$4 - 19$x$2 - 30$x$. Two numbers were represented by $x$ and $x$ + 2. Find the expressions that were used to represent the other two numbers.
 a. ($x$ + 3) and ($x$ - 5) b. ($x$ + 3) and ($x$ + 5) c. ($x$ - 3) and ($x$ - 5) d. ($x$ - 3) and ($x$ + 5)

9.
Alice expressed three consecutive odd integers in a distinct way. The product of the three integers is given by the polynomial $x$3 - 9$x$2 + 23$x$ - 15. One of her integers is expressed as $x$ - 3. Find the other expressions did Alice use for the other two integers.
 a. ($x$ + 1) and ($x$ + 5) b. ($x$ - 1) and ($x$ + 1) c. ($x$ + 5 ) and ($x$ - 5) d. ($x$ - 1) and ($x$ - 5)

Find the sum of the polynomials 2$y$2 + 5$y$ and 4$y$2 - 3$y$.
 a. 6$y$2 + 2$y$ b. 6$y$2 - 2$y$ c. $y$2 - 2$y$ d. 3$y$2 - $y$