Polynomials Test

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Polynomials Test - 19

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Weekly Quiz Competition

Question 1
1 / -0

What is the degree of the following polynomial expression:
$$\dfrac{5}{3} x^{3} + 7x + 16$$

A
2

B
3

C
1

D
$$\dfrac{5}{3}$$

Solution

Clearly, the degree of the polynomial expression $$\frac{5}{3} x^{3} + 7x + 16$$ is $$3$$.
The degree of a polynomial is the highest degree of its monomials (individual terms) with non-zero coefficients. The degree of a term is the sum of the exponents of the variables that appear in it, and thus is a non-negative integer.
Question 2
1 / -0

What is the degree of the following polynomial expression:
$$4x^{2} - 3x + 2$$

A
$$1$$

B
$$2$$

C
$$3$$

D
$$4$$

Solution

The degree of the polynomial is equal to the highest power of the variable present in the expression. Here, $$x$$ is the variable and its highest power is $$2$$ in the term $$4x^2$$. Hence, the degree of the polynomial is equal to $$2.$$
Question 3
1 / -0

Find the degree of the following polynomial:
$$-\dfrac{3}{2}$$

A
$$1$$

B
$$2$$

C
$$0$$

D
Cannot be determined

Solution

Given polynomial can be rewritten as $$-\dfrac32 x^0$$ so, the highest degree of the variable present in the polynomial is $$0$$ hence the degree of the polynomial is equal to $$0.$$
Question 4
1 / -0

Find the degree of following polynomial
$$4x-\sqrt{5}$$

A
$$\dfrac{1}{2}$$

B
1

C
2

D
0

Solution

The degree is the value of the greatest exponent of any expression (except the constant) in the polynomial.
Given,
$$4x-\sqrt{5}$$
There are 2 terms $$4p-\sqrt{5}$$,so it is a binomial and the polynomial has variable $$x$$ as the highest degree of all the terms.
Therefore,
Degree is $$1$$
Question 5
1 / -0

Find the degree of following polynomial $$5$$

A
$$5$$

B
$$1$$

C
$$0$$

D
Constant

Solution

The degree is the value of the greatest exponent of any expression (except the constant) in the polynomial.
Given,
$$5$$
Since there is $$1$$ term $$5$$, it is a monomial and the polynomial has no variable.
Therefore,
Degree is $$0$$
Question 6
1 / -0

Use identities to solve: $$(97)^{2}$$

A
$$9,659$$

B
$$9,409$$

C
$$9,009$$

D
$$9,209$$

Solution

$$(97)^2$$
$$=(100-3)^2$$
using, $$(a-b)^2=a^2-2ab+b^2$$
$$=(100)^2-2(100)3+(3)^2$$
$$=10000-600+9$$
$$=9409$$
Question 7
1 / -0

Use the identity $$ (a+b)(a-b) = a^2-b^2$$ to evaluate:
$$33\times 27 $$.

A
$$891$$

B
$$881$$

C
$$981$$

D
$$841$$

Solution

We know, $$ 33 \times 27 = (30 + 3) \times (30 - 3) $$ .

Applying the formula $$ (a+b)(a-b) = { a }^{ 2 }-{ b }^{ 2 } $$, where $$ a = 30 , b = 3 $$,
we get,
$$ 33 \times 27 = (30 + 3) \times (30 - 3) = { 30 }^{ 2 }-{ 3 }^{ 2 } = 900 - 9 = 891 $$ .

Therefore, option $$A$$ is correct.
Question 8
1 / -0

Find the zero of the polynomial given below:
$$p(x) = 9x - 3$$.

A
$$\dfrac{6}{7}$$

B
$$\dfrac{1}{2}$$

C
$$\dfrac{1}{3}$$

D
$$\dfrac{7}{3}$$

Solution

Given, $$p(x) = 9x - 3$$.
to find the zero of a polynomial we need to equal that polynomial to zero.
thus, $$p(x)=0$$

$$\Rightarrow9x-3=0$$

$$\Rightarrow x=\dfrac{3}{9}$$

$$\Rightarrow x=\dfrac{1}{3}$$.

Therefore, option $$C$$ is correct.
Question 9
1 / -0

Degree of the polynomial $$4x^4+0x^3+0x^5+5x+7$$ is

A
$$4$$

B
$$5$$

C
$$3$$

D
$$7$$

Solution

Clearly, the highest power of $$x$$ is $$4$$.
Hence, the degree of given polynomial is $$4$$.
Option A is correct.
Question 10
1 / -0

If p(x)= $$x^3-4x^2+5x-2$$, then p(2) is:

A
$$0$$

B
$$3$$

C
$$5$$

D
$$8$$

Solution

Let $$f(x)=x^3-4x^2+5x-2$$
Now, $$f(2)=2^3-4\times2^2+5\times2-2$$
$$=8-16+10-2=0$$
Since, $$f(2)=0$$.
Then we can say that, $$2$$ is a zero of $$f(x)=x^3-4x^2+5x-2$$.

Therefore, option $$A$$ is correct.

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Polynomials Test - 19

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Polynomials Test - 19

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Question 1

2

3

1

$$\dfrac{5}{3}$$

Solution

Question 2

$$1$$

$$2$$

$$3$$

$$4$$

Solution

Question 3

$$1$$

$$2$$

$$0$$

Cannot be determined

Solution

Question 4

$$\dfrac{1}{2}$$

1

2

0

Solution

Question 5

$$5$$

$$1$$

$$0$$

Constant

Solution

Question 6

$$9,659$$

$$9,409$$

$$9,009$$

$$9,209$$

Solution

Question 7

$$891$$

$$881$$

$$981$$

$$841$$

Solution

Question 8

$$\dfrac{6}{7}$$

$$\dfrac{1}{2}$$

$$\dfrac{1}{3}$$

$$\dfrac{7}{3}$$

Solution

Question 9

$$4$$

$$5$$

$$3$$

$$7$$

Solution

Question 10

$$0$$

$$3$$

$$5$$

$$8$$

Solution

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