Polynomials Class 9 Worksheet Maths Chapter 2

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Multiple Choice Questions

Q1: If x/y + y/x = -1 and (xy, ≠ 0), the value of x³ – y³ is
(a) 1
(b) -1
(c) 0
(d) 2
Ans: (c)
x/y + y/x = -1
x² + y² = − xy
or
x² + y² + xy = 0
Now x³ – y³ = (x − y) (x² + y² + xy) = (x − y) × 0 = 0
Hence (c) is the correct answer

Q2: If p + q + r = 0 ,then the value of
(a) 1
(b) 3
(c) -1
(d) 0
Ans: (b)
Now we know that p³ + q³ + r³ − 3pqr = (p + q + r) (p² + q² + r² − pq − qr − pr)
as p + q + r = 0
p³ + q³ + r³ − 3pqr = 0 or p³ + q³ + r³ = 3pqr
Now

Hence (b) is the correct answer.

Q3: The product of (x + a) (x + b) is
(a) x² + (a + b)x + ab
(b) x² - (a - b)x + ab
(c) x² + (a - b)x + ab
(d) x² + (a - b)x + ab
Ans: (a)
(x+a) (x+b) = x(x+b) + a(x+b)
$=\; x^2\; +\; bx\; +\; ax\; +\; ab$=x² + bx + ax + ab
$=\; x^2\; +\; (a\; +\; b)x\; +\; ab$=x² + (a+b)x + ab

Q4: The value of (x + 2y + 2z)² + (x - 2y - 2z)² is
(a) 2x² + 8y² + 8z²
(b) 2x² + 8y² + 8z² + 8xyz
(c) 2x² +8y² + 8z² - 8yz
(d) 2x² + 8y² + 8z² + 16yz
Ans: (d)

Q5: The value of f(x) = 5x−4x2+3 when x = -1, is: 
(a) 3 
(b) -12 
(c) -6

(d) 6
Ans: (c)

To find the value of $f(x)\; =\; 5x\; -\; 4x^2\; +\; 3$f(x) = 5x − 4x²+ 3 when $x\; =\; -1$x = −1, follow these steps:

Substitute x = −1 into the equation:

$f(-1)\; =\; 5(-1)\; -\; 4(-1)^2\; +\; 3$f (−1) = 5(−1) − 4(−1)² + 3

f(−1) = −5 −4 + 3

f(−1) = −6

True or False

Q1: P(x) = x - 1 and g(x) =x² - 2x  + 1 . p(x) is a factor of g(x)
Ans: True, as g(1) = 0

Q2: The factor of 3x² – x - 4 are (x + 1)(3x - 4)
Ans: True, we can get this by split method

Q3: Every linear polynomial has only one zero
Ans: True

Q4: Every real number is the zero’s of zero polynomial
Ans: True

Q5: A binomial may have degree 4
Ans: True, example x⁴ + 1

Q6: 0, 2 are the zeroes of x²- 2x
Ans: True

Q7: The degree of zero polynomial is not defined
Ans: True

Answer the following Questions

Q1: Is 3x^1/2 - 4x + 15 a polynomial of one variable?
Ans: No. it is not a polynomial

Q2: Is ∛x - √2x a polynomial
Ans: No. It is not a polynomial

Q3: What will be the degree of polynomials 30x⁵ - 15x² + 40
Ans: Degree of Polynomial is 5

Q4: Is (y²)^1/2 + 2√3 a polynomial of one variable?
Ans: Yes it is a polynomial of one variable

Q5: What will be the coefficient of x³ in 9x³ - 5x + 20.
Ans: The coefficient of x³ is 9

Q6: Show that x = 1 is a root of the polynomial 3x³ - 4x² + 8x - 7
Ans: On putting x = 1
X = 1 is root of polynomial
3x³ - 4x² + 8x - 7 
3(1)³  - 4(1)² + 8(1) - 7 
3 - 4 + 8 - 7 = 0
X = 1 is root of polynomial