Exercise 1

Find a and b if the polynomial x5 − ax + b is divisible by x² − 4.

Exercise 2

Determine the coefficients a and b for the polynomial x³ + ax² + bx + 5 if it is divisible by x² + x + 1.

Exercise 3

Find the value of k if the division of 2x² − kx + 2 by (x − 2) gives a remainder of 4.

Exercise 4

Determine the value of m if 3x² + mx + 4 has x = 1 as one of its roots.

Exercise 5

Find a fourth degree polynomial that is divisible by x² − 4 and is annuled by x = 3 and x = 5.

Exercise 6

Calculate the value of a for which the polynomial x³ − ax + 8 has the root x = −2. Also, calculate the other roots of the polynomial.

Solution of exercise Solved Polynomial Word Problems

Solution of exercise 1

Find a and b if the polynomial x5 − ax + b is divisible by x² − 4.

x² − 4 = (x +2) · (x − 2)

P(−2) = (−2)5 − a · (−2) + b = 0

−32 +2a +b = 0         2a +b = 32

  P(2) = 25 − a · 2 + b = 0

32 − 2a +b = 0          − 2a +b = −32

Solution of exercise Solved Polynomial Word Problems

Solution of exercise 2

Determine the coefficients a and b for the polynomial x³ + ax² + bx + 5 if it is divisible by x² + x + 1.

b − a = 0            −a + 6 = 0

a = 6           b = 6

Solution of exercise Solved Polynomial Word Problems

Solution of exercise 3

Find the value of k if the division of 2x² − kx + 2 by (x − 2) gives a remainder of 4.

P(2) = 2 · 2² − k · 2 +2 = 4

10 − 2k = 4        − 2k = − 6       k = 3

Solution of exercise Solved Polynomial Word Problems

Solution of exercise 4

Determine the value of m if 3x² + mx + 4 has x = 1 as one of its roots.

P(1) = 3 · 1² + m · 1 + 4 = 0

3 + m + 4 = 0              m = − 7

Solution of exercise Solved Polynomial Word Problems

Solution of exercise 5

Find a fourth degree polynomial that is divisible by x² − 4 and is annuled by x = 3 and x = 5.

(x − 3) · (x − 5) · (x² − 4) =

(x² −8 x + 15) · (x² − 4) =

= x4 − 4x² − 8x³ +32x + 15x² − 60 =

= x4 − 8x³ + 11x² +32x − 60

Solution of exercise Solved Polynomial Word Problems

Solution of exercise 6

Calculate the value of a for which the polynomial x³ − ax + 8 has the root x = −2. Also, calculate the other roots of the polynomial.

P(−2) = (−2)³ − a · (−2) +8 = 0        −8 + 2a +8 = 0         a= 0

(x + 2) · (x² − 2x + 4)

x² − 2x + 4 = 0

It has no more real roots.

Did you like the article?

1 Star2 Stars3 Stars4 Stars5 Stars (No Ratings Yet)
Loading...

Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.

Did you like
this resource?

Bravo!

Download it in pdf format by simply entering your e-mail!

{{ downloadEmailSaved }}

Your email is not valid