Class 9th math notes

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Q10/10: Which of the following polynomials has (x + 1) as a factor?

Q9/10: If p(x) = x^4 + ax^3 - 7x^2 - 8x + b is divisible by (x^2 - 4), find the values of a and b.

Q8/10: Find the value of x^3 - 8y^3 - 36xy - 216 if x = 2y + 6.

Q7/10: If x = 2 is a root of the polynomial p(x) = 2x^2 - 3x + 7a, find the value of a.

Q6/10: Factorise the expression 8x^3 + 27y^3 using standard algebraic identities.

Q5/10: Which of the following expressions represents a cubic polynomial?

Q4/10: What is the constant term in the expansion of the product (x + 4)(x - 5)?

Q3/10: A gardener's rectangular garden has an area represented by 3x^2 - 12x. What could be the possible dimensions (length and breadth) of the garden?

Q2/10: A company makes cubic boxes. The volume is given by V(x) = x^3 - 6x^2 + 11x - 6. If the height is (x-1), what are the possible expressions for length and width?

Q1/10: A rectangular swimming pool has an area represented by 2x^2 + 5x - 3. If its length is (2x - 1), what is its breadth?

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Q10/10: Assertion (A): x+1 is a factor of x^3 + 1. Reason (R): If p(a) = 0, then x-a is a factor of p(x).

Q9/10: Assertion (A): The degree of the polynomial (x^2+1)(x-3) is 3. Reason (R): The degree of a polynomial is the highest power of the variable in it.

Q8/10: Find the remainder when the polynomial x^4 + x^3 - 2x^2 + x + 1 is divided by x - 1.