REMAINDER THEOREM PROBLEMS WITH UNKNOWNS WORKSHEET

Problem 1 :

Given that x − 2 is a factor of the polynomial

x³ − kx² − 24x + 28

find k and the roots of this polynomial.

Solution

Problem 2 :

Find the quadratic whose roots are −1 and 1/3 and whose value at x = 2 is 10.

Solution

Problem 3 :

Consider the polynomial p(x) = x³ − 4x² + ax − 3.

(a) Find a if, when p(x) is divided by x + 1, the remainder is −12.

(b) Find all the factors of p(x).

Solution

Problem 4 :

Consider the polynomial

h(x) = 3x³ − kx² − 6x + 8

(a) Given that x − 4 is a factor of h(x), find k and find the other factors of h(x).

Solution

Problem 5 :

Find the quadratic which has a remainder of −6 when divided by x − 1, a remainder of −4 when divided by x − 3 and no remainder when divided by x + 1

Solution

Problem 6 :

Find the value of a if x − 3 is a factor of f(x)= x³ - 11x + a

Solution

Problem 7 :

Find the value of k if f(x) = 3(x² + 3x - 4) - 8(x - k) is divisible by x.

Solution

Problem 8 :

If x − 2 is a factor of polynomial 

p(x) = a(x³ - 2x) + b(x² - 5)

which of the following must be true ?

a)  a + b = 0    b) 2a - b = 0    c) 2a + b = 0  d)  4a - b = 0

Solution