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 true, and R is the correct explanation of A.
Both A and R are true, but R is not the correct explanation of A.
A is true, but R is false.
A is false, but R is true.
Factorisation
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Answer
Since, the highest value of power of x in the polynomial x3 + 2x2 - x - 2 is 3.
Thus,
x3 + 2x2 - x - 2 is a polynomial of degree 3.
∴ Assertion (A) is true.
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.
∴ Reason (R) is true.
Both A and R are true, but R is not the correct explanation of A.
Hence, Option 2 is the correct option.
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