Class 9 Polynomial Maths DPP
CLASS - 9
Comprehensive Chapter Practice: HOTS & NCERT Questions
Q 1. If p(x) = x² - 2√2x + 1, then p(2√2) is equal to:
(a) 0 (b) 1 (c) 4√2 (d) 8√2 + 1
Q 2. One of the zeroes of the polynomial 2x² + 7x - 4 is:
(a) 2 (b) ½ (c) -1/2 (d) -2
Q 3. The roots of the polynomial equation 3x³ - 12x = 0 are:
(a) 3, 2, -2 (b) 3, 0, 4
(c) 0, 2, -2 (d) 3, 0, 2
Q 4. The polynomial p(x) = xm + x, where m > 1, when divided
by (x - a), leaves remained 6. Given that a is a positive integer,
what is the value of m?
(a) 2 (b) 3 (c) 5 (d) 6
[HOTS] [TERM by CBSE]
Q 5. If (x + 2) and (x - 1) are factors of the polynomial
10x² + px + q, then p/q is:
(a) -1/2 (b) ¼ (c) -1 (d) -2
Q 6. The remainder when x³ + 3x² + 3x + 1 is divided by 5 + 2x is:
(a) -27/8 (b) 23/5 (c) 27/8
(d) -27/11
Q 7. The coefficient of x in the expansion of (x + 3)³ is:
(a) 1 (b) 9 (c) 18 (d) 27
Q 8. The value of the polynomial 5x - 4x² + 3, when x = -1 is:
(a) -6 (b) 6 (c) 2 (d) -2
Q 9. Which of the following algebraic expression is a polynomial in
one variable?
(a) 7x² - 2/x (b) 7x² - 3x + √2
(c) (x-2)(x-4)/x (d) 7x² - xy + 5y + 2
Q 10. Zero of the polynomial p(x), where p(x) = ax + 1, a ≠ 0 is:
(a) -1/a (b) 0 (c) 1/a (d) -a
Q 11. If x³ + y³ + z³ = 0, then
(a) x³ + y³ + z³ = 0 (b) x³ + y³ + z³ - 27xyz
(c) (x + y + z)³ = 27xyz (d) x + y + z = 3xyz
Q 12. If 49x² - b = (7x + 1/2)(7x - 1/2), then the value of b is
(a) 0 (b) 1/√2 (c) ¼ (d) 1/2
Q 13. If a² + b² + c² = 200 and ab + bc + ca = 28, then the value of
a + b + c is:
(a) 156 (b) 256 (c) 16 (d) 320
[HOTS]
Q 14. Which of the following is a factor of (x + y)³ - (x³ + y³)?
(a) x² + xy + 2xy (b) x² + y² - xy
(c) xy² (d) 3xy
[HOTS]
Q 15. If a + b + c = 0, then the value of a³ + b³ + c³ is:
(a) 0 (b) abc (c) 2abc (d) 3abc
[HOTS]
Q 16. If the polynomial x³ + 3x² + 3x + 1 is divided by x - 5, then
the remainder is:
(a) 1 (b) 216 (c) – 216 (d) 27
[HOTS]
Q 17. If x + k is a factor of the polynomial x³ + kx² - 2x + k + 5, then the value of k is:
(a) -5/3 (b) 5 (c) – 5 (d) 5/2
[HOTS]
Q 18. If a² + b² + 2(ab + bc + ca) is given expression, then:
(i) (a + b) is one of the factor.
(ii) (a + b + 2c) is one of the factor.
(iii) (a - b) is one of the factor.
(iv) (a + b - 2c) is one of the factor.
Choose the correct option from the following:
(a) (i) and (ii) (b) Only (i)
(c) Only (ii) (d) (iii) and (iv)
[HOTS]
Q 19. If the polynomial 2x³ - 3x² + 5x - 3 is divided by x + 2, then
which of the following options hold true:
(i) Remainder = 10
(ii) Remainder = 7
(iii) Quotient = 2x² - 4x + 5x - 5
(iv) Quotient = 2x² + 5x - 5
Choose the correct option from the following:
(a) Only (ii) (b) (ii) and (iii)
(c) (ii) and (iv) (d) Only (iv)
[HOTS]
Q 20. If the polynomial x³ - 3x² + 4x + 50 is divided by x + 3, then
(i) Coefficient of x² in quotient is 2.
(ii) Coefficient of x in quotient is - 6.
(iii) Remainder is - 16.
(iv) Remainder is 16.
Choose the correct option from the following:
(a) Only (i) (b) Only (iv)
(c) (ii) and (iii) (d) (i) and (iv)
[HOTS]
Q 21. Write the degree of each of the following polynomials:
(i) - 5x³ + 14x² + (7x / 2) (ii) 15t - √7 / 2
(iii) 33 (iv) 9x³ - 19x + 13x (v) 100
(vi) y³ (1 - y³)
[HOTS]
Q 22. Check whether 0 and 2 are zeroes of the polynomial x² - 2x.
[NCERT]
Q 23. Find the value of the polynomial 4 + x³ - x + 2x² at:
(i) x = 0 (ii) x = -1 (iii) x = 3
[HOTS]
Q 24. Check whether p(x) is a multiple of g(x) or not:
(i) p(x) = x³ - 5x² + 4x - 3, g(x) = x - 2
(ii) p(x) = 2x³ - 11x² - 4x + 5, g(x) = 2x + 1
[NCERT Exemplar]
Q 25. Find the value of k, if x - 1 is a factor of 4x³ + 3x² - 4x + k.
[HOTS]
Q 26. Find the value of m so that 2x - 1 is a factor of
8x⁴ + 4x³ - 16x² + 10x + m.
[HOTS]
Q 27. What is the possible expression for the dimensions of the
cuboid whose volume is 3x² - 12x?
Q 28. Factorise the following using suitable identity:
(i) a² + 4b² + 25c² + 4ab + 20bc + 10ac
(iii) x12 – y12
Q 29. Find the products using suitable identities:
(i) (x + 3y + 5z)(x² + 9y² + 25z² - 3xy - 15yz - 5zx)
(ii) (-z + x - 2y)(x² + 4y² + z² + 2xy - 2yz + zx)
[NCERT Exemplar]
Q 30. Simplify:
((a² - b²)³ + (b² - c²)³ + (c² - a²)³)/((a - b)³ + (b - c)³ + (c - a)³)
[HOTS]
Q 31. Find the value of x³ - 8y³ - 36xy - 216, when x = 2y + 6.
[HOTS]
Q 32. If x + y + z = 8 and xy + yz + zx = 20, find the value so
x³ + y³ + z³ - 3xyz.
[HOTS]
Q 33. (i) If a + b = 8 and ab = 6, find the value of a³ + b³.
(ii) If a - b = 6 and ab = 20, find the value of a³ - b³.
[HOTS]
Q 34. Find the roots of the following polynomial equations:
(i) 3x - 10 = 0 (ii) 2√7x - 11 = 0 (iii) (x - 3)(x + 2) = 0
[HOTS]
Q 35. Simplify:
(i) (a + b + c)² - (a - b + c)²
(ii) (a + b + c)² + (a - b + c)² + (a + b - c)²
(iii) (2x + p - c)² - (2x - p + c)²
[HOTS]
Q 36. If x = 4/3 is a zero of the polynomial f(x) = 6x³ - 11x² + kx –
20, find the value of k.
[HOTS]
Q 37. Factorise each of the following expressions by splitting the
middle term:
(i) 9y²/2 + 4y + 2 (ii) y²/2 + 9/2 y + 10
(iii) x²/2 + 6x + 18 (iv) 2x²/3 - 17x/3 - 28
[HOTS]
Q 38. Verify if 1 and - 3 are zeroes of the polynomial
3x³ + 5x² - 11x + 3. If yes, then factorise the polynomial.
[HOTS]
Q 39. If x + 1/x = 4, find the values of
(i) x² + 1/x² (ii) x⁴ + 1/(x⁴) (iii) x³ + 1/x³
(iv) x - 1/x [HOTS]
Q 40. If x² - 1 is a factor of p(x) = ax⁴ + bx³ + cx² + dx + e, show
that a + c + e = b + d = 0.
[HOTS]
Q 41. Factorise each of the following expressions by splitting the
middle term:
(i) x⁴ + 19x² - 150 (ii) x⁴ + 3x² - 28
(iii) x⁴ + 4x² + 3 [HOTS]
Q 42. Factorise the cubic polynomial 2x³ - x² - 13x - 6.
[HOTS]
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