Chapters

- Exercise 1
- Exercise 2
- Exercise 3
- Exercise 4
- Exercise 5
- Exercise 6
- Solution of exercise Solved Polynomial Word Problems
- Solution of exercise 1
- Solution of exercise Solved Polynomial Word Problems
- Solution of exercise 2
- Solution of exercise Solved Polynomial Word Problems
- Solution of exercise 3
- Solution of exercise Solved Polynomial Word Problems
- Solution of exercise 4
- Solution of exercise Solved Polynomial Word Problems
- Solution of exercise 5
- Solution of exercise Solved Polynomial Word Problems
- Solution of exercise 6

## Exercise 1

Find * a* and

*if the polynomial x*

**b**^{5}− ax + b is divisible by x² − 4.

## Exercise 2

Determine the coefficients * a* and

*for the polynomial x³ + ax² + bx + 5 if it is divisible by x² + x + 1.*

**b**## 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

*if the polynomial x*

**b**^{5}− 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) = 2^{5} − 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

*for the polynomial x³ + ax² + bx + 5 if it is divisible by x² + x + 1.*

**b**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) =

= x^{4} − 4x² − 8x³ +32x + 15x² − 60 =

= x^{4} − 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.

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