Worksheet Solutions: Polynomials

# Polynomials Class 9 Worksheet Maths Chapter 2

### 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)

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

Ans: (d)

Q5: Find the value of (a3 b3 c3 - 3abc)/(ab + bc + c - a2 - b2 - c), when a = -5, b = -6 c = -10.
(a) 1
(b) -1
(c) 2
(d) -2

Ans: (a)

### True or False

Q1: P(x) = x - 1 and g(x) =x- 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

Q1: Is 3x1/2 - 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 xin 9x3 - 5x + 20.
Ans: 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

The document Polynomials Class 9 Worksheet Maths Chapter 2 is a part of the Class 9 Course Mathematics (Maths) Class 9.
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## Mathematics (Maths) Class 9

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## FAQs on Polynomials Class 9 Worksheet Maths Chapter 2

 1. What is a polynomial?
A polynomial is a mathematical expression that consists of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication. It can have one or more terms, with each term having a variable raised to a non-negative integer power.
 2. How do you determine the degree of a polynomial?
The degree of a polynomial is determined by the highest power of the variable in the expression. To find the degree, identify the term with the highest exponent and that will be the degree of the polynomial.
 3. What are the different types of polynomials?
There are several types of polynomials, including: - Monomial: a polynomial with only one term. - Binomial: a polynomial with two terms. - Trinomial: a polynomial with three terms. - Quadratic: a polynomial of degree 2. - Cubic: a polynomial of degree 3. - Quartic: a polynomial of degree 4. - Quintic: a polynomial of degree 5.
 4. How do you add or subtract polynomials?
To add or subtract polynomials, combine like terms. Like terms are terms with the same variables raised to the same power. Add or subtract the coefficients of these like terms while keeping the variables and exponents the same.
 5. Can a polynomial have negative exponents?
No, a polynomial cannot have negative exponents. In a polynomial, the exponents must be non-negative integers. Negative exponents would make the expression a non-polynomial.

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