CBSE Class 9 Mental Maths Polynomials Worksheet

Question. What is the degree of the polynomial 4− y² ?
Answer : 2

Question. What is the degree of the polynomial 5x³ + 4x² + 7x ?
Answer : 3

Question. Whether the following polynomials are linear, quadratic or cubic polynomials.
(i) x − x³ (ii) y + y² + 4 (iii) 3t
Answer : (i) Cubic (ii) Quadratic
(iii) linear

Question. What is the value of the polynomial −4x² + 7 x−5 when x = –3?
Answer : -62

Question. If f(x) = 2x³ −3x² + 12 then find f(2).
Answer : 16

Question. What is the degree of the polynomial (y³−2)(y² +11).
Answer : 5

Question. If P(y) = y² − y+1then what is value of P(3).
Answer : 7

Question. What is the zero of the polynomial P(x) = x + 5?
Answer : -5

Question. What is the Coefficient of x in the expression 2x + y + Z ?
Answer : 1/2

Question. What is the Coefficient of x in the expression x² √5x 2 ?
Answer : –√5

Question. What is the degree of the polynomial 20?
Answer : zero

Question. What is the standard form of y² + 6y + 9 + 4y⁴ ?
Answer : 4y⁴ + y² + 6y + 9

Question. What is the standard form of q² + 4q⁸ −q⁶ ?
Answer : 4q⁸ − q⁶ + q²

Question. What is the remainder when p(x) = x³ − ax² + 6x−a is divided by x – a?
Answer : 5a

Question. Find the remainder when x⁵¹ + 51 is divided by x + 1.
Answer : 50

Question. Find the value of K if x + 3 is a factor of 3x² + kx + 6.
Answer : 11

Question. Express 8x³ + 60x² + 150x + 125 as a cube of binomial.
Answer : (2x + 5)³

Question. Factorize9 p² − 16q² .
Answer : (3p + 4q) (3p − 4q)

Question. Facrorize x(x² + y² − z²) − z(x² + y² − z² ).
Answer : (x−z) (x² + y² – z²)

Question. Expand (x + 5y)³ .
Answer : x³ + 125y³ + 15x² y + 75xy²

Question. Expand (2x −7)²
Answer : 8x³ − 343 − 84x² + 294x

Question. Expand (3x −1)²
Answer : 9x² – 6x + 1

Question. Expand (x + 2)²
Answer : x² + 4x + 4

Question. Factorize 50x² – 72y²
Answer : 2(5x + 6y) (5x − 6y)

Question. Factorize m² + 2√3m + 3
Answer : (m + √3)²

Question. Find the zeros of polynomials x² +14x + 40 .
Answer : (−4,−10)

Question. What is the product of Zero’s of polynomials (x + 8 )(x − 10).
Answer : -80

Question. Facroeize 9x² - y²/100
Answer : (3x + y/10) (3x - y/10)

Question. What is the degree of polynomial 4y² − 4y + 1.
Answer : 2

Question. Factorize 8a³ − b³ − 12a²b + 6ab² .
Answer : (2a - b)³

Question. Factorize 8x³ + 27 y³ + 36x² y + 54xy²
Answer : (2x +3y)³

Question. Factorize 36a² + 60ab + 25b² .
Answer : (6a + 5b)²

Question. Find the product (x−5)(x+4).
Answer : x² − x − 20

Question. Find the product (x−3)(x−7).
Answer : x² −10x + 21

Question. Find the product (x+6)(x+8).
Answer : x² + 14x + 48

Question. Find the remainder when p(x) = x³ + x² + x + 1 is divided by g(x) = x + 1.
Answer : 0

Question. If p(x) = x⁴ +3x³ + 3x² + x+1 and g(x) = x+1 then find the remainder when p(x) is divided by g(x).
Answer : 1

Question. Find the value of K if x - 2 is the factor of x³ −2x² − x + k .
Answer : k = 2

Question. Find the value of K if x + 1 is the factor of x³ −kx² − 9x−5.
Answer : k = 3

Question. Find the value of K if x - 1 is factor of 3x⁴ −kx³ −3x + 4 .
Answer : k = 4

Question. Find the value of K if x + 1 is facror of 3x² + x+k .
Answer : k = -2

Question. What is the Coefficient of x² in the polynomial 3x³ − 15x² + 10x−2 .
Answer : -15

Question. Find the value of p(x) = x² −4x + 7 when x = 3.
Answer : 4

Question. Find the value of f (-3/2) when f(x) = 4x² + 3x + 7/2
Answer : 8

Question. If f(x) = x² −5x−14 find the value of f(7).
Answer : 0

Question. Find the zeros of the polynomial x² −15x−34 .
Answer : 17, -2

Question. What should be added to the polynomial x² 5x 4x . so that 3 is a zero of the polynomial.
Answer : 2

Question. Which of the number 3,2,-2,1 are zeros of the polynomial x² −4 ?
Answer : 2, -2

Question. Find the quotient when x² −7x + 12 is divided by (x - 3).
Answer : x - 4

Question. Find the polynomial whose zeros are √2 and − √2 .
Answer : x² −2