Add the polynomial expressions 3−2p−5p2 and p4−3p+4.

Question

Add the polynomial expressions 3−2p−5p2 and p4−3p+4.

A. p4−5p2−5p+7

B. −4p2−5p+7

C. p4−5p2−6p+7

D. −5p2−4p+7

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10 answers
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Answer 1

Bot GPT 3.5 answered
1 year ago

The polynomial expressions are 3−2p−5p^2 and p^4−3p+4.

To add the polynomials, we combine like terms.

The p^4 term is only present in the second polynomial.
The -5p^2 term is present in both polynomials. Its coefficients are -5 and 0, so the sum is -5p^2.
The -2p term is only present in the first polynomial.
The -3p term is present in both polynomials. Its coefficients are 0 and -3, so the sum is -3p.
The 3 and 4 are constants.

The sum of the terms can therefore be written as:
p^4 - 5p^2 - 3p + 3 + 4

Combining the constants, we have:
p^4 - 5p^2 - 3p + 7

Therefore, the sum of the polynomial expressions is:
p^4 - 5p^2 - 3p + 7

Answer: C. p^4 - 5p^2 - 3p + 7

Answer 2

Anonymous answered
1 year ago

What is (3x2−2)+(11−5x)

A. 2x2−9

B. −2x2+9

C. 3x2−5x+9

D. 3x2+5x−9

Answer 3

Bot GPT 3.5 answered
1 year ago

The given expression is (3x^2−2)+(11−5x).

To solve this expression, we need to combine like terms.

First, we combine the terms within the parentheses: 3x^2−2+11−5x.

Next, we combine the constant terms: -2+11 = 9.

Finally, we combine the x terms: 3x^2−5x.

Putting it all together, we have 3x^2−5x+9.

Therefore, the answer is C. 3x^2−5x+9.

Answer 4

Anonymous answered
1 year ago

Which operation shows that polynomials are a closed system under addition?

A. (2x2+6x+1)+(3x2+3x+9)=(2x2+3x+1)+(3x2+6x+9)

B. (2x2+6x+1)+(3x2+3x+9)=(2x2+3x2)+(6x+3x)+(1+9)

C. (2x2+6x+1)+(3x2+3x+9)=5x2+9x+10

D. (2x2+6x+1)+(3x2+3x+9)=−x2+3x−8

Answer 5

Bot GPT 3.5 answered
1 year ago

To show that polynomials are a closed system under addition, we need to demonstrate that adding two polynomials will always result in another polynomial.

A polynomial is an expression consisting of variables, coefficients, and exponents, with operations of addition and multiplication. When we add two polynomials, we combine like terms, resulting in a new polynomial.

Let's examine the options:

A. (2x^2+6x+1)+(3x^2+3x+9)=(2x^2+3x+1)+(3x^2+6x+9)
This option shows that we can rearrange the terms and add them in any order, which preserves the polynomial structure.

B. (2x^2+6x+1)+(3x^2+3x+9)=(2x^2+3x^2)+(6x+3x)+(1+9)
This option shows how the terms can be combined by adding like terms. The result maintains the polynomial form.

C. (2x^2+6x+1)+(3x^2+3x+9)=5x^2+9x+10
This option shows the correct addition of like terms producing a polynomial with no missing or extraneous terms.

D. (2x^2+6x+1)+(3x^2+3x+9)=−x^2+3x−8
This option shows a different result with a missing term.

Based on the explanations provided, we can conclude that the correct option showing that polynomials are a closed system under addition is:

C. (2x^2+6x+1)+(3x^2+3x+9)=5x^2+9x+10

Answer 6

Anonymous answered
1 year ago

Which operation shows that polynomials are a closed system under subtraction?

A. (2x2+6x+1)−(3x2+3x+9)=(2x2+6x−4)−(3x2+3x+4)

B. (2x2+6x+1)−(3x2+3x+9)=−x2+3x−8

C. (2x2+6x+1)−(3x2+3x+9)=2x2+6x+1−3x2−3x−9

D. (2x2+6x+1)−(3x2+3x+9)=5x2+9x+10

Answer 7

Bot GPT 3.5 answered
1 year ago

To show that polynomials are a closed system under subtraction, we need to demonstrate that subtracting two polynomials will always result in another polynomial.

A polynomial is an expression consisting of variables, coefficients, and exponents, with operations of addition, subtraction, and multiplication. When we subtract two polynomials, we combine like terms, resulting in a new polynomial.

Let's examine the options:

A. (2x^2+6x+1)−(3x^2+3x+9)=(2x^2+6x−4)−(3x^2+3x+4)
This option shows how to rearrange the terms and subtract them in any order without affecting the polynomial structure.

B. (2x^2+6x+1)−(3x^2+3x+9)=−x^2+3x−8
This option shows the correct subtraction of like terms producing a polynomial with no missing or extraneous terms.

C. (2x^2+6x+1)−(3x^2+3x+9)=2x^2+6x+1−3x^2−3x−9
This option shows how the terms can be combined by subtracting like terms. The result maintains the polynomial form.

D. (2x^2+6x+1)−(3x^2+3x+9)=5x^2+9x+10
This option shows a different result with missing terms.

Based on the explanations provided, we can conclude that the correct option showing that polynomials are a closed system under subtraction is:

B. (2x^2+6x+1)−(3x^2+3x+9)=−x^2+3x−8

Answer 8

Anonymous answered
1 year ago

Which operation shows that polynomials are a closed system under addition?

A. (5x2+2x+1)+(−2x2+6x+4)=(5x2−2x2)+(2x+6x)+(1+4)

B. (5x2+2x+1)+(−2x2+6x+4)=(−2x2+2x+4)+(5x2+6x+1)

C. (5x2+2x+1)+(−2x2+6x+4)=−3x2+8x−3

D. (5x2+2x+1)+(−2x2+6x+4)=3x2+8x+5

Answer 9

Bot GPT 3.5 answered
1 year ago

To show that polynomials are a closed system under addition, we need to demonstrate that adding two polynomials will always result in another polynomial.

A polynomial is an expression consisting of variables, coefficients, and exponents, with operations of addition and multiplication. When we add two polynomials, we combine like terms, resulting in a new polynomial.

Let's examine the options:

A. (5x^2+2x+1)+(−2x^2+6x+4)=(5x^2−2x^2)+(2x+6x)+(1+4)
This option shows that we can rearrange the terms and add them in any order, which preserves the polynomial structure.

B. (5x^2+2x+1)+(−2x^2+6x+4)=(−2x^2+2x+4)+(5x^2+6x+1)
This option shows how the terms can be combined by adding like terms. The result maintains the polynomial form.

C. (5x^2+2x+1)+(−2x^2+6x+4)=−3x^2+8x−3
This option shows the correct addition of like terms producing a polynomial with no missing or extraneous terms.

D. (5x^2+2x+1)+(−2x^2+6x+4)=3x^2+8x+5
This option shows a different result with a missing sign.

Based on the explanations provided, we can conclude that the correct option showing that polynomials are a closed system under addition is:

C. (5x^2+2x+1)+(−2x^2+6x+4)=−3x^2+8x−3

Answer 10

Explain Bot answered
11 months ago

To add polynomial expressions, we need to combine like terms. Like terms are terms that have the same variable raised to the same exponent.

Let's break down the given polynomial expressions:

3 − 2p − 5p^2

p^4 − 3p + 4

To add these expressions, we need to combine the terms with the same exponent.

Starting with the highest degree term, which is p^4, we have p^4 + 0p^2 + 0p + 0.

Moving on to the next highest degree term, which is -5p^2, we add -5p^2 + 0p + 0.

Then, we combine the terms with the next highest degree, which is -2p, resulting in -2p + 0.

Finally, we add the constant terms, which are 3 + 4, resulting in 7.

Putting it all together, the sum of the polynomial expressions is p^4 - 5p^2 - 2p + 7.

Therefore, the correct answer is C. p^4 - 5p^2 - 2p + 7.