1 Marks Question

Question 11 Mark

Which of the following expressions are not polynomials. $3\text{y}^3-\sqrt{5}\text{y}+9$

Answer

$3\text{y}^3-\sqrt{5}\text{y}+9$ is not a polynomial because the powers of variable y are non negative integers.

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Question 21 Mark

Write the degree of the following polynomials.
$20 x^3+12 x^2 y^2-10 y^2+20$

Answer

The degree of the polymonial $20 x^3+12 x^2 y^2-10 y^2+20$ is $4$.

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Question 31 Mark

Write of the following polynomials in the standard form. Also write their degree. $\Big(\text{a}^3-\frac{3}{8}\Big)\Big(\text{a}^3+\frac{16}{17}\Big)$

Answer

$\Big(\text{a}^3-\frac{3}{8}\Big)\Big(\text{a}^3+\frac{16}{17}\Big)=\text{a}^6+\frac{77}{136}\text{a}^3-\frac{6}{17}$ Standard form of the given polynomial can be expressed as: $\Big(\text{a}^6+\frac{77}{136}\text{a}^3-\frac{6}{17}\Big)$ or $\Big(-\frac{6}{17}+\frac{77}{136}\text{a}^3+\text{a}^6\Big)$ The degree of the polynomial is $6.$

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Question 41 Mark

Write of the following polynomials in the standard form. Also write their degree.
$\left(x^3-1\right)\left(x^3-4\right)$

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Question 51 Mark

Divide $6 x^3 y^2 z^2$ by $3 x^2 y z$.

Answer

$\frac{6\text{x}^3\text{y}^2\text{z}^2}{3\text{x}^2\text{yz}}=\frac{6\times\text{x}\times\text{x}\times\text{x}\times\text{y}\times\text{y}\times\text{z}\times\text{z}}{3\times\text{x}\times\text{x}\times\text{y}\times\text{z}}$
$=2\text{x}^{(3-2)}\text{y}^{(2-1)}\text{z}^{(2-1)}=2\text{xyz}$

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Question 61 Mark

Write the degree of the following polynomials.
$5 x^2=3 x+2$

Answer

The degree of polymonial $5 x^2=3 x+2$ is $2$.

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Question 71 Mark

Which of the following expressions are not polynomials. $\sqrt{\text{ax}}+\text{x}^2-\text{x}^3$

Answer

$\sqrt{\text{ax}}+\text{x}^2-\text{x}^3$ is not a polynomial because $\frac{1}{2}$ is the power of variable $x$ is not a non negative integer.

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Question 81 Mark

Which of the following expressions are not polynomials.
$3x^{-2}$ + $2x{-1}$+ $4x$ + $5$

Answer

$3x^{-2}$ + $2x{-1}$+ $4x$ + $5$ is not a polynomial because $-2$ and $-1$ are the powers of variable $x$ are not non negative integer.

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Question 91 Mark

Write of the following polynomials in the standard form. Also write their degree. $\Big(\text{a}+\frac{3}{4}\Big)\Big(\text{a}+\frac{4}{3}\Big)$

Answer

$\Big(\text{a}+\frac{3}{4}\Big)\Big(\text{a}+\frac{4}{3}\Big)=\text{a}^2+\frac{25}{12}\text{a}+1$ Standard form of the given polynomial can be expressed as: $\Big(\text{a}^2+\frac{25}{12}\text{a}+1\Big)$ or $\Big(1+\frac{25}{12}\text{a}+\text{a}^2\Big)$ The degree of the polynomial is $2.$

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Question 101 Mark

Write the degree of the following polynomials$.5$

Answer

$5$ is a constant polynomial and its degree is $0.$

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Question 111 Mark

Write the degree of the following polynomials.
$\frac{1}{2}\text{y}^7-12\text{y}^6+48\text{y}^5-10$

Answer

The degree of the polymonial $\frac{1}{2}\text{y}^7-12\text{y}^6+48\text{y}^5-10\text{ is }7.$

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Question 121 Mark

Write the degree of the following polynomials.
$3x^3$+ $1$

Answer

The degree of the polymonial $3x^3$+ $1$ is $3$.

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Question 131 Mark

Write of the following polynomials in the standard form. Also write their degree.
$a^2 + 4 + 5a^6$

Answer

Standard form of the given polynomial can be expressed as: $(5a^6 + a^2 + 4)$ or $(4 + a^2 + 5a^6)$
The degree of the polynomial is $6.$

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Question 141 Mark

Write of the following polynomials in the standard form. Also write their degree.
$x^2 + 3 + 6x + 5x^4$

Answer

Standard form of the given polynomial can be expressed as:
$(5x^4 + x^2 + 6x + 3)$ or $(3 + 6x + x^2 + 5x^4)$ The degree of the polynomial is $4.$

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Question 151 Mark

Which of the following expressions are not polynomials.
$x^2 + 2x^{-2}$

Answer

$x^2 + 2x^{-2}$ is not a polynomial beause $-2$ is the power of variable $x$ is not a non negative integer.

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Question 161 Mark

Write of the following polynomials in the standard form. Also write their degree.
$(y^3 - 2)(y^3 + 11)$

Answer

$(y^3 - 2)(y^3 + 11)$ = $y^6 + 9y^3 - 22$
Standard form of the given polynomial can be expressed as:$(y^6 + 9y^3 - 22)$ or $(-22 + 9y^3 + y^6)$
The degree of the polynomial is $6$.

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Question 171 Mark

Which of the following expressions are not polynomials. $\text{ax}^{\frac{1}{2}}+\text{ax}+9\text{x}^2+4$

Answer

$\text{ax}^{\frac{1}{2}}+\text{ax}+9\text{x}^2+4$ is not a polynomial because $\frac{1}{2}$ is the power of variable $x$ is not a non negative integer.

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Question 181 Mark

Write the degree of the following polynomials.
$2x^2 + 5x^2 - 7$

Answer

Correction: It is $2x^2 + 5x^2 - 7$ instead of $2x^2 + 7$. The degree of the polymonial $2x^3 + 5x^2 - 7$ is $3$.

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Question 191 Mark

Write the degree of the following polynomials.
$2x + x^2 - 8$

Answer

The degree of the polymonial $2x + x^2 - 8$ is $2$.

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