**Assertion and Reason Questions for Class 9 Maths Chapter 2 Polynomials**

** Directions: **Choose the correct answer out of the following choices :

(a) Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.

(b) Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.

(c) Assertion is correct statement but Reason is wrong statement.

(d) Assertion is wrong statement but Reason is correct statement.

**Q.1. Assertion : **3x^{2} + x – 1 = (x + 1) (3x – 2) + 1.**Reason : **To factorise ax^{2} + bx + c, write b as sumof two numbers whose product is ac.

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Answer: (a)**Q.2. Assertion : **The value of 593 × 607 is 359951.**Reason :** (a + b) (a – b) = a^{2} – b^{2}

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Answer: (a)**Q.3. Assertion : **The degree of the polynomial(x^{2} – 2)(x – 3)(x + 4) is 3.**Reason :** A polynomial of degree 3 is called a cubic polynomial.

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Answer: (d)**Q.4. Assertion : **The expression 3x^{4} – 4x^{3/2} + x^{2} = 2is not a polynomial because the term – 4x^{3/2} contains a rational power of x.**Reason : **The highest exponent in various terms of an algebraic expression in one variable is called its degree.

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Answer: (b)**Q.5.. Assertion : **If 2x^{2} – 32 is the volume of a cuboid, then length of cuboid can be x – 8.**Reason : **Volume of a cuboid = l × b × h.

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Answer: (d)**Q.6. Assertion :** –7 is a constant polynomial.**Reason :** Degree of a constant polynomial is zero.

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Answer: (a)**Questions for practice:**

*Directions: *

(a) Both assertion and reason are true and reason is the correct explanation of assertion.

(b) Both assertion and reason are true but reason is not the correct explanation of assertion.

(c) Assertion is true but reason is false.

(d) Assertion is false but reason is true

1. Assertion : If f(x) = 3x^{7} – 4x^{6} + x + 9 is a polynomial, then its degree is 7.

Reason : Degree of a polynomial is the highest power of the variable in it.

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Answer:2. Assertion : (x + 2) and (x – 1) are factors of the polynomial x^{4} + x^{3} + 2x^{2} + 4x – 8.

Reason : For a polynomial p(x) of degree ≥ 1, x – a is a factor of the polynomial p(x) if and only if p(a) ≥1 .

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Answer:3. Assertion : 3x^{2} + x – 1 = (x + 1)(3x – 2x) + 1.

Reason : If p(x) and g(x) are two polynomials such that degree of p(x) ≥ degree of g(x) and g(x) ≥ 0 then we can find polynomials q(x) and r(x) such that p(x) = g(x) q(x) + r(x) , where r(x) = 0 of degree of r(x) <degree of g(x).

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Answer:4. Assertion : (x + 2) is a factor of x^{3} + 3x^{2 }+ 5x + 6 . and of 2x + 4

Reason : If p(x)be a polynomial of degree greater than or equal to one, then (x – a) is a factor of p(x), if p(a) = 0

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Answer:5. Assertion : The remainder when p(x) = x^{3} – 6x^{2} + 2x – 4 is divided by (3x – 1) is – 107/27.

Reason : If a polynomial p(x) is divided by ax –b , the remainder is the value of p(x) at x = b/a.

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Answer:6. Assertion : If (x + 1) is a factor of f(x) = x^{2} + ax + 2 then a = – 3 .

Reason : If (x – a ) is a factor of p(x), if p(a) = 0.

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Answer:7. Assertion : If f(x) = x^{4} + x^{3} – 2x^{2} + x + 1 is divided by (x – 1) , then its remainder is 2.

Reason : If p(x) be a polynomial of degree greater than or equal to one, divided by the linear polynomial x – a , then the remainder is p(- a ) .

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Answer:8. Assertion : The degree of the polynomial (x – 2 )(x – 3 )(x + 4) is 4.

Reason : The number of zeroes of a polynomial is the degree of that polynomial.

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Answer:9. Assertion : If p(x) = ax + b , a≠ 0 is a linear polynomial, then x = – b/a is the only zero of p(x).

Reason : A linear polynomial has one and only one zero.