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Olegator [25]
3 years ago
15

Which algebraic expression is a polynomial with a degree of 2?

Mathematics
2 answers:
olganol [36]3 years ago
7 0

Answer:D

Step-by-step explanation:

uysha [10]3 years ago
6 0
Given the question "<span>Which algebraic expression is a polynomial with a degree of 2?" and the options:
1). 4x^3-2x
2). 10x^2- \sqrt{x}
3). 8x^3+ \frac{5}{x} + 3
4). 6x^2-6x + 5

A polynomial </span><span>is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

</span><span>The degree of a polynomial is the highest exponent of the terms of the polynomial.

For option 1: </span><span>It contains no fractional or negative exponent, hence it is a polynomial. But the highest exponent of the terms is 3, hence it is not of degree 2.

For opton 2: It contains a fractional exponent which violates the definition of a polynomial, hence, it is not a polynomial.
i.e. 10x^2- \sqrt{x} =10x^2- x^{ \frac{1}{2} }

For option 3: </span><span>It contains a negative exponent which violates the definition of a polynomial, hence, it is not a polynomial.
i.e. 8x^3+ \frac{5}{x} + 3=8x^3+5x^{-1}+3

For option 4: It contains no fractional or negative exponent, hence it is a polynomial. Also, the highest exponent of the terms is 2, hence it is of degree 2.
</span>
Therefore, <span>6x^2-6x + 5 s a polynomial with a degree of 2. [option 4]</span>
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James determined that these two expressions were equivalent expressions using the values of x = 4 and x = 6. Which statements ar
GaryK [48]

Answer:

The expressions 7x + 4 and 3x + 5 + 4x = 1 are equivalent for every value of x.

Step-by-step explanation:

Expressions - 7x + 4 and 3x + 5 + 4x = 1.

1. When x = 2, both expressions have a value of 18. Let's find out:

1st expression : 7(2) + 4 = 14+4 = 18

2nd expression : 3(2) + 5 + 4(2) = 1

or 6 + 5 + 8 - 1 = 18

Values of both the expressions is 18, hence it is correct statement.

2.The expressions are only equivalent for x = 4 and x = 6.

This is incorrect statement as we just calculated above that the expressions are equivalent for x = 2. Hence, it is incorrect.

3. The expressions have equivalent values for any value of x.

Say, x = 0, then,

7x + 4 = 7 (0) + 4 = 4 and,

3x + 5 + 4x - 1 =  3(0) + 5 + 4(0) - 1  = 5-1 = 4

The statement holds.

Let's try again for x = 12,

7x + 4 = 7(12) + 4 = 88 and,

3x + 5 + 4x - 1 =  3(12) + 5 + 4(12) - 1  = 36 + 5 + 48 -1 =  88

Let's try again for x = 13,

7x + 4 = 7(13) + 4 = 95 and,

3x + 5 + 4x - 1 =  3(13) + 5 + 4(13) - 1  = 39 + 5 + 52 -1 =  95

Clearly, it holds for every value of x, whether it is odd or even. Hence, it is correct statement.

_______________________________________________________

Trick: 7x + 4 = 0....(1) and,

3x + 5 + 4x = 1

Rearranging the terms of above expression, we get,

(3x + 4x) + (5 - 1) =0

or 7x + 4 = 0...(2)

clearly both (1) & (2) are equivalent.

_____________________________________________________

4 0
2 years ago
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