PRACTICE PROBLEMS ON DIVIDING POLYNOMIALS

Use synthetic division to divide the polynomials given below then find the quotient and remainder.

Problem 1 :

(x² + 8x + 1) ÷ (x - 4)

Solution

Problem 2 :

(4x² - 13x - 5) ÷ (x - 2)

Solution

Problem 3 :

(2x² - x + 7) ÷ (x + 5)

Solution

Problem 4 :

(x³ - 4x + 6) ÷ (x + 3)

Solution

Problem 5 :

(x² + 9) ÷ (x - 3)

Solution

Problem 6 :

(3x³ - 5x² - 2) ÷ (x - 1)

Solution

Problem 7 :

(x⁴ – 5x³ - 8x² + 13x - 12) ÷ (x - 6)

Solution

Problem 8 :

(x⁴ + 4x³ + 16x - 35) ÷ (x + 5)

Solution

Problem 9 :

Describe and correct the error in using synthetic division to divide x³ − 5x + 3 by x − 2.

Solution

Problem 10 :

Describe and correct the error in using synthetic division to divide x³ − 5x + 3 by x − 2.

Solution

Problem 11 :

Jordan divided the polynomial x⁴ + x - 6 in to the polynomial p(x) yesterday. Today his work is smudged and he cannot read p(x) or most his answer. The only part he could read was the remainder x + 4. His teacher wants him to find p(-3), what is p(-3) ?

Solution

Problem 12 :

The volume V of the rectangular prism is given by V = 2x³ + 17x² + 46x + 40. Find an expression for the missing dimension.

Solution

Problem 13 :

You divide two polynomials and obtain the result

(5x² − 13x + 47) − [102/(x + 2)]

What is the dividend? How did you find it.

Solution

Problem 14 :

What is the value of k such that 

(-x⁴ + 5x² + kx - 8) ÷ (x - 4)

has a remainder of 0?

Solution

Divide the following polynomials using long division.

Problem 1 :

(x² + x - 17) ÷ (x - 4)

Solution

Problem 2 :

(3x² - 14x – 5) ÷ (x - 5)

Solution

Problem 3 :

(x³ + x² + x + 2) ÷ (x² - 1)

Solution

Problem 4 :

(7x³ + x² + x) ÷ (x² + 1)

Solution

Problem 5 :

(5x⁴ – 2x³ - 7x² - 39) ÷ (x² + 2x - 4)

Solution

Problem 6 :

(4x⁴ + 5x - 4) ÷ (x² - 3x - 2)

Solution

Problem 7 :

The expression (6x - 5)/(x + 2) is equivalent to which of the follwoing ?

a)  6 - [17/(x + 2)]          b)  6 + [7/(x + 2)]

Solution

Problem 8 :

When 3x² + 4 is dividied by x - 1, the result is A + [7/(x - 1)]. What is A in terms of x ?

a)  3x - 4      b)  3x - 3     c)  3x + 3     d)  3x + 4

Solution

Problem 9 :

If the expression (5x² - 4x + 1)/(x - 2) is written in the form 5x + 6 + [B/(x - 2)], where B is constant what is the value of B ?

a)  3      b)  13     c)  -4     d)  -13

Solution

Problem 10 :

If the expression (2x² - 5x + 1)/(x - 3) is written in the equivalent form 2x + 1 + [R/(x - 3)], what is the value of R

a)  4      b)  2     c)  -4     d)  -3

Solution

Problem 11 :

f(x) = 3x³ - kx² + 5x + 2

In the polynomial f(x) defined above, k is constant. If f(x) is divisible by x - 2. What is the value of k ?

a)  12    b)  9    c)  6      d)  3

Solution

Problem 12 :

The table above gives the value of polynomial p(x) for some values of x. Which of the following must be a factor of p(x) ?

a) x + 1      b)  x - 1     c)  x - 4      d)  x - 5

Solution

Problem 13 :

For the polynomial p(x), p(2) = 0, which of the following must be true about p(x) ?

a)  2x is a factor of p(x)      b)  2x - 2 is a factor of p(x)

c)  x - 2 is a factor of p(x)        d)  x + 2 is a factor of p(x)

Solution