Question

whether (x-5)is factor of (x3-x2-x-1) is or not
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Answer 1

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Let P(x) = x³ - x² - x - 1

Let g(x) = x - 5, then

⟹ g(x) = 0

⟹ x - 5 = 0

⟹ x = 5

By Factor theorm, p(x) must be exactly divisible by g(x) and would hence give the result as 0.

Now,

⟶ p(5) = {(5)³ - (5)² - 5 - 1}

⟶ p(5) = ( 125 - 25 - 5 - 1 )

⟶ p(5) = 125 - 31

⟶ p(5) = 94

The value is not equal to 0

hence x³ - x² - x - 1 is not a factor of x - 5

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Answer 2

We have been how to check if (x-5) is a factor of the given number which is x³ - x² - x - 1 .

For finding the solution we need to follow down the given steps :

1. Find value of (x)
2. Substituting x in the polynomial
3. Simplify
4. Check the remainder

Following the steps ; we get :

Value of x :

→ x - 5 = 0

→ x = 0 + 5

→ x = 5

Substituting :

→ p(x) = x³ - x² - x - 1

→p(5) = 5³ - 5² - 5 - 1 .

Simplification :

→p(5) = 5³ - 5² - 5 - 1

→p(5) = 125 - 25 - 5 - 1

→p(5) = 100 - 5 - 1

→p(5) = 95 - 1

→p(5) = 94

p(5) is not a factor of given polynomial as ; when a number is a polynomial ; the remainder is zero .