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ICSE Class 10 Mathematics Question 43 of 49

Multiple-Choice Questions — Question 43

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Question 43

Assertion (A) : x3 + 2x2 - x - 2 is a polynomial of degree 3.

Reason (R) : x + 2 is a factor of the polynomial.

  1. Both A and R are correct, and R is the correct explanation for A.

  2. Both A and R are correct, and R is not the correct explanation for A.

  3. A is true, but R is false.

  4. Both A and R are true.

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.