CHECK IF THE GIVEN IS ZERO OF POLYNOMIAL WORKSHEET

For each of the following cubic equations one root is given. Determine the other roots of each cubic.

Problem 1 :

x³ + 3x² – 6x – 8 = 0 has a root at x = 2.

Solution

Problem 2 :

x³ + 2x² – 21x + 18 = 0 has a root at x = 3.

Solution

Problem 3 :

x³ + 4x² + 7x + 6 = 0 has a root at x = -2.

Solution

Problem 4 :

2x³ + 9x² + 3x – 4 = 0 has a root at x = -4.

Solution

For each of the following cubic equations use synthetic division to determine if the given value of x is a root of the equation. Where it is, determine the other roots of the equation.

Problem 5 :

Is x = -2 a root of the equation x³ + 9x² + 26x + 24 = 0 ?

Solution

Problem 6 :

Is x = 4 a root of the equation x³ - 6x² + 9x + 1 = 0 ?

Solution

Problem 7 :

Is x = -1 a root of the equation x³ + 6x² + 3x - 5 = 0 ?

Solution

Problem 8 :

Is x = 2 a root of the equation x³ + 2x² - 20x + 24 = 0 ?

Solution

Use the remainder theorem to find f(k).

Problem 1 :

k = 2; f(x) = x² - 2x + 5

A) -5     B) -3    C) -13     D) 5

Solution

Problem 2 :

k = -3; f(x) = x² + 2x + 2

A) 1     B) -13     C) 5     D) -17

Solution

Problem 3 :

k = -2; f(x) = 3x³ - 7x² - 3x + 3

A) 14     B) -55     C) -43     D) -5

Solution

Problem 4 :

k = 4; f(x) = x³ - 2x² + 5x - 2

A) 54     B) 50     C) -78     D) -76

Solution

Problem 5 :

k = 2; f(x) = 9x⁴ + 10x³ + 6x² - 6x + 16

A) 360     B) 500     C) 252     D) 36

Solution

Problem 6 :

k = 5; f(x) = x³ - 3x² - 4x - 5

A) 35     B) 25    C) -225     D) -220

Solution

Problem 7 :

Using the remainder theorem find the remainders obtained when x³ + (kx + 8)x + k is divided by x + 1 and x - 2. Hence, find k if the sum of the two remainders is 1.

Solution