Question -One of the factors of x5-x-1 is1 2 x2-x-12 x3-x2-13 x2-2 x2-14 x3-x2-1

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Byju's Answer

Standard IX

Mathematics

Factor Theorem

Question :One...

Question

Question :

One of the factors of x⁵+x+1 is

(1) 2x² - x - 1

(2) x³ - x²+ 1

(3) x² - 2x² + 1

(4) x³ + x² + 1

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Solution

x^5+x+1
= x^5 - x^4 + x^4 - x^3 + x^ 3 - x^2 +x^2+x+1
=x^4(x-1) + x^3(x-1) + x^2 (x - 1)+ x^ 2+ x +1
=(x-1)(x^4+x^3+x^2)+(x^2+x+1)
=(x-1)(x^2)(x^2+x+1)+(x^2+x+1)
=(x^2+x+1)(1+(x-1)*x^2)
=(x^2+x+1)(x^3-x^2+1)
So
x^5+x+1=(x^3-x^2+1)(x^2+x+1)

therefore (x^3-x^2+1) is a factore

so option (2) is the right answer

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Question : One of the factors of x5+x+1 is (1) 2x2 - x - 1 (2) x3 - x2 + 1 (3) x2 - 2x2 + 1 (4) x3 + x2 + 1

Question :

One of the factors of x⁵+x+1 is

(1) 2x² - x - 1

(2) x³ - x²+ 1

(3) x² - 2x² + 1

(4) x³ + x² + 1