Exercise 1 Page 537

To check which of the given values is not a solution to x^3-3x^2-25x+75=0, we will substitute them to the given equation and check which one gives a false statement. Let's start by substituting 5 for x. The result is a true statement, so 5 is indeed a solution of the given equation. Now we will check x=3.

x^3-3x^2-25x+75=0

Substitute

x= 3

3^3-3( 3)^2-25( 3)+75 ? = 0

▼

Simplify

CalcPow

Calculate power

27-3(9)-25(3)+75 ? = 0

Multiply

Multiply

27-27-75+75 ? = 0

AddSubTerms

Add and subtract terms

0 = 0 ✓

We found that 3 is also a solution, so let's try the third possibility, x=- 3.

x^3-3x^2-25x+75=0

Substitute

x= - 3

( - 3)^3-3( - 3)^2-25( - 3)+75 ? = 0

▼

Simplify

CalcPow

Calculate power

- 27-3(9)-25(- 3)+75 ? = 0

Multiply

Multiply

- 27-27+75+75 ? = 0

AddSubTerms

Add and subtract terms

96 = 0 *

The result is a false statement, so - 3 is not a solution of the given equation. To make sure that we are right, we will check the last option, x=- 5.

x^3-3x^2-25x+75=0

Substitute

x= - 5

( - 5)^3-3( - 5)^2-25( - 5)+75 ? = 0

▼

Simplify

CalcPow

Calculate power

- 125-3(25)-25(- 5)+75 ? = 0

Multiply

Multiply

- 125-75+125+75 ? = 0

AddSubTerms

Add and subtract terms

0 = 0 ✓

We found that 3, 5, and - 5 are the solutions of x^3-3x^2-25x+75=0, but - 3 is not a solution. Therefore, the correct option is C.