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Multiple Choice Questions

Consider the following statements I x 3 is the factor of x3 2x2 3x 8 II x ndash 2 is the f...........

Mathematics (NDA) Algebra

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Consider the following statements

I. x + 3 is the factor of x³ + 2x² + 3x + 8.

II. x – 2 is the factor of x³ + 2x² + 3x + 8.

Which of the statements given above is/are correct?

Only I

Only II

Both I and II

Neither I nor II

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Explanation:

Put x = –3 in equation x³ + 2x² + 3x + 8
= (–3)³ + 2(–3)² + 3(–3) + 8
= –10 ≠ 0
So, (x + 3) is not the factor of x³ + 2x² + 3x + 8
Similarly, put x = 2 in above equation
= (2)³ + 2(2)² + 3(2) + 8
= 30 ≠ 0
So, (x – 2) is also not the factor of x³ + 2x² + 3x + 8.