Polynomials - Rajasthan Board (RBSE) STD 9 MATHS Questions

Q 1M.C.Q1 Mark

Write the correct answer in the following:
Which one of the following is a polynomial?

$\frac{\text{x}^2}{2}-\frac{2}{\text{x}^2}$
$\sqrt{2\text{x}-1}$
$\text{x}^2+\frac{3\text{x}^{\frac{3}{2}}}{\sqrt{\text{x}}}$
$\frac{\text{x}-1}{\text{x}+1}$

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Q 2M.C.Q1 Mark

Write the correct answer in the following:
$\sqrt{2}$ is a polynomial of degree.

2
0
1
$\frac{1}{2}$

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Q 3M.C.Q1 Mark

Write the correct answer in the following: One of the zeroes of the polynomial $2x^2 + 7x - 4$ is.

A
$2$
✓
$\frac{1}{2}$
C
$-\frac{1}{2}$
D
$-2$

Answer: B.

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Q 4M.C.Q1 Mark

Write the correct answer in the following: The coefficient of $x$ in the expansion of $(x + 3)^3$ is.

A
$1$
B
$9$
C
$18$
✓
$27$

Answer: D.

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Q 5M.C.Q1 Mark

Write the correct answer in the following: The value of $249^2 - 248^2$ is.

A
$1^2$
B
$477$
C
$487$
✓
$497$

Answer: D.

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Q 6True False[1 Marks ]1 Mark

Write whether the following statement are True or False.
A binomial can have atmost two terms.

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Q 7True False[1 Marks ]1 Mark

Write whether the following statement are True or False. Every polynomial is a binomial.

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Q 8True False[1 Marks ]1 Mark

Write whether the following statement are True or False. A polynomial cannot have more than one zero.

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Q 9True False[1 Marks ]1 Mark

Write whether the following statement are True or False.
Zero of a polynomial is always 0.

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Q 10True False[1 Marks ]1 Mark

Write whether the following statement are True or False. The degree of the sum of two polynomials degree $5$ is always $5$.

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Q 111 Marks Question1 Mark

Determine the degree of the following polynomial:
–10

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Q 121 Marks Question1 Mark

Determine the degree of following polynomial:
2x - 1

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Q 131 Marks Question1 Mark

Classify the following polynomials as polynomials in one variable, two variables etc. $x^2 - 2xy + y^2 + 1$

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Q 141 Marks Question1 Mark

Factorise: $2x^2 - 7x - 15$

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Q 151 Marks Question1 Mark

Verify whether the following are True or False:
$\frac{-4}{5}$ is a zero of 4 - 5y

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Q 162 Marks Questions2 Marks

By actual division, find the quotient and the remainder when the first polynomial is divided by the second polynomial : $x^4 + 1; x - 1$

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Q 172 Marks Questions2 Marks

Expand the following: $\Big(4-\frac{1}{3{\text{x}}}\Big)^3$

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Q 182 Marks Questions2 Marks

Factorise the following: $8\text{p}^3+\frac{12}{5}\text{p}^2+\frac{6}{25}\text{p}+\frac{1}{125}$

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Q 192 Marks Questions2 Marks

Expand the following: $(3a - 2b)^3$

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Q 202 Marks Questions2 Marks

Factorise the following: $16x^2 + 4y^2 + 9z^2 - 16xy - 12yz + 24xz$

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Q 213 Marks Question3 Marks

Find the value of the polynomial $3x^3 - 4x^2 + 7x - 5,$ when $x = 3$ and also when $x = -3.$

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Q 223 Marks Question3 Marks

Find the following product: $(2x - y + 3z) (4x^2 + y^2 + 9z^2 + 2xy + 3yz - 6xz)$

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Q 233 Marks Question3 Marks

Determine which of the following polynomials has $x - 2 a$ factor: $3x^2 + 6x - 24 , 4x^2+ x – 2$

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Q 243 Marks Question3 Marks

For the polynomial $\frac{\text{x}^3+2\text{x}+1}{5}-\frac{7}{2}\text{x}^2-\text{x}^6,$ write.

A
The degree of the polynomial.
B
The coefficient of $x^3.$
✓
The coefficient of $x^{6.}$
D
The constant term.

Answer: C.

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Q 253 Marks Question3 Marks

Check whether $p(x)$ is a multiple of $g(x)$ or not: $p(x) = 2x^3 - 11x^2 - 4x + 5, g(x) = 2x + 1$

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Q 264 Marks Questions4 Marks

Prove that $(a + b + c)^3 - a^3 - b^3 - c^3 = 3(a + b )(b + c)(c + a).$

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Q 274 Marks Questions4 Marks

Multiply$ x^2 + 4y^2 + z^2 + 2xy + xz - 2yz$ by $(-z + x - 2y).$

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Q 284 Marks Questions4 Marks

Without actual division, prove that $2x^4 - 5x^3 + 2x^2 - x + 2$ is divisible by $x^2 - 3x + 2.$
$[$Hint: Factorise $x^2 - 3x + 2]$

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Q 294 Marks Questions4 Marks

The polynomial $p(x) = x^4 - 2x^3 + 3x^2 - ax + 3a - 7$ when divided by $x + 1$ leaves the remainder $19.$ Find the values of a. Also find the remainder when $p(x)$ is divided by $x + 2.$

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Polynomials MATHS - Polynomials

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