Mathematics
Assertion (A) : x3 + 2x2 - x - 2 is a polynomial of degree 3.
Reason (R) : x + 2 is a factor of the polynomial.
Both A and R are correct, and R is the correct explanation for A.
Both A and R are correct, and R is not the correct explanation for A.
A is true, but R is false.
Both A and R are true.
Factorisation
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Answer
x3 + 2x2 - x - 2 is a polynomial of degree 3.
By factor theorem,
(x - a) is a factor of f(x) if f(a) = 0.
x + 2 = 0
x = -2
Substituting x = -2 in x3 + 2x2 - x - 2, we get :
⇒ (-2)3 + 2(-2)2 - (-2) - 2
⇒ -8 + 2(4) + 2 - 2
⇒ -8 + 8 + 2 - 2
⇒ 0.
Hence, Option 4 is the correct option.
Answered By
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