Polynomials - Gujarat Board (GSEB) STD 9 Maths Questions

Q 1M.C.Q1 Mark

Write the correct answer in the following: If $x+1$ is a factor of the polynomial $2 x^2+k x$, then the value of $k$ is.

A
$-3$
B
$4$
✓
$2$
D
$-2$

Answer: C.

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Q 2M.C.Q1 Mark

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

A
$\frac{\text{x}^2}{2}-\frac{2}{\text{x}^2}$
B
$\sqrt{2\text{x}-1}$
✓
$\text{x}^2+\frac{3\text{x}^{\frac{3}{2}}}{\sqrt{\text{x}}}$
D
$\frac{\text{x}-1}{\text{x}+1}$

Answer: C.

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Q 3M.C.Q1 Mark

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

A
$2$
✓
$0$
C
$1$
D
$\frac{1}{2}$

Answer: B.

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Q 4M.C.Q1 Mark

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

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

Answer: B.

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Q 5M.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 6True False[1 Marks ]1 Mark

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

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Q 7True 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 8True 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 9True 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 10True 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 111 Marks Question1 Mark

Using suitable identity, evaluate the following:
$999^2$

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Q 121 Marks Question1 Mark

Classify the following as a constant, linear, quadratic and cubic polynomial:
$2-x^2+x^3$

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Q 131 Marks Question1 Mark

Classify the following as a constant, linear, quadratic and cubic polynomial: $5\text{t}-\sqrt{7}$

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Q 141 Marks Question1 Mark

Which of the following expression are polynomials? $\sqrt{3}\text{x}^2-2\text{x}$

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Q 151 Marks Question1 Mark

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

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Q 162 Marks Questions2 Marks

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

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Q 172 Marks Questions2 Marks

If $a, b, c$ are all non-zero and $a+b+c=0$, prove that $\frac{a^2}{b c}+\frac{b^2}{c a}+\frac{c^2}{a b}=3$.

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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:
$(3 a-2 b)^3$

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Q 202 Marks Questions2 Marks

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

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Q 213 Marks Question3 Marks

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

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Q 223 Marks Question3 Marks

Factorise:
$x^3+x^2-4 x-4$

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Q 233 Marks Question3 Marks

If $x+2 a$ is a factor of $x^5-4 a^2 x^3+2 x+2 a+3$, find $a$.

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Q 243 Marks Question3 Marks

Find the following product: $(2 x-y+3 z)\left(4 x^2+y^2+9 z^2+2 x y+3 y z-6 x z\right)$

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Q 253 Marks Question3 Marks

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

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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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