Mathematics, 05.01.2021 06:50 Toady8432

Which of the following are polynomials? A. x^2 + x + 1/x^2 + 1
B. 2/x^3 + x + 1/2
C. 2/3x^2 + x + 1
D. x^2/3 + 0x + 1
E. x^3 + 2x + square root of 2

Which of the following are polynomials?

A. x^2 + x + 1/x^2 + 1
B. 2/x^3 + x + 1/2
C. 2/3x^2 + x +

Answers: 1

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Answers

Answer from: genyjoannerubiera

The polynomials are:

$\frac{2}{3}$ x² + x + 1 ⇒ C

x³ + 2x +√2 ⇒ E

Step-by-step explanation:

A polynomial: is an expression consisting of variables and coefficients, with the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables

A polynomial never division by a variableA polynomial could be one term, and it could be just a constant

Let us solve the question

∵ The polynomial never division by a variable

∵ Answer A and B have a division in variable ⇒ ( $\frac{1}{x^{2}+1 }$ , $\frac{2}{x^{3}}$ )

∴ Answers A and B are not polynomials

∵ The polynomial has integer exponents of variables

∵ Answer D has a fraction exponent of x ⇒ $x^{\frac{2}{3}}$

∴ Answer D is not a polynomial

∵ $\frac{2}{3}$ x² + x + 1 has a non-negative integer exponent of x

∵ There is no division by x

∴ $\frac{2}{3}$ x² + x + 1 is a polynomial

∵ x³ + 2x +√2 has a non-negative integer exponent of x

∵ There is no division by x

∴ x³ + 2x +√2 is a polynomial

∴ The polynomials are $\frac{2}{3}$ x² + x + 1 and x³ + 2x +√2

Answer from: Quest

6/20

step-by-step explanation:

Answer from: Quest

$a_1 = 1$ , and

$a_{n+1} = a_n + (n + 1)$ for $n \ge 1$

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote $a_1 = 1$ , $a_2 = 3$ , $a_3 = 6$ , so that we can call

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from $a_1 = 1$ , to get to $a_2 = 3$ , we add $2(=1+1)$

from $a_2 = 3$ , to get to $a_3 = 6$ , we add $3 (=2+1)$

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

$a_1 = 1$ , and $a_{n+1} = a_n +(n + 1)$ for $n \ge 1$

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Which of the following are polynomials? A. x^2 + x + 1/x^2 + 1
B. 2/x^3 + x + 1/2
C. 2/...

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