Mathematics, 05.10.2020 14:01 vctorsurfs327

Select each statement that is true for all polynomials. When two polynomials are added, the sum is always a polynomial.
When two polynomials are divided, the quotient is always a
polynomial.
When two polynomials are multiplied, the product is always a
polynomial.
When two polynomials are subtracted, the difference is always a
polynomial.

Answers: 3

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Answers

The statement which is true for all polynomials is; When two polynomials are multiplied, the product is always a polynomial.

Discussion:

The sum of or difference between two polynomials may not necessarily be a polynomial. This is so because, the addition or subtraction of the polynomials may yield a function other than a polynomial.

The same for division of polynomials in which case the quotient may not always be a polynomial.

However, when two polynomials are multiplied, the product is always a polynomial.

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Answer from: spaigenicole

Option 3

Step-by-step explanation:

Analyzing All Options:

Option 1: Sum of 2 polynomials is always a polynomial;

This isn't always true; Take for instance:

(2x^3 - 3x^2 + 4x + 5) + (-2x^3 + 3x^2 - 4x + 9)

2x^3 - 3x^2 + 4x + 5 -2x^3 + 3x^2 - 4x + 9

-2x^3+2x^3 + 3x^2- 3x^2 + 4x- 4x + 5 + 9

The result in this case isn't a polynomial

Option 2: The quotient of two polynomials is always a polynomial

This isn't always true; Take for instance:

$\frac{4x^2 + 2x+ 2}{2x^2 + x + 1}$

$=\frac{2(2x^2 + x + 1)}{2x^2 + x + 1}$

The result in this case isn't a polynomial

Option 3: The multiplication of two polynomials is always a polynomial

This is always true; Take for instance:

(2x^3 - 3x^2 + 4x + 5) * (-2x^3 + 3x^2 - 4x + 9)

Expand this, and you get a polynomial

Option 4: Subtraction of 2 polynomials is always a polynomial;

This isn't always true; Take for instance:

(2x^3 - 3x^2 + 4x + 5) - (2x^3 - 3x^2 + 4x + 9)

2x^3 - 3x^2 + 4x + 5 - 2x^3 + 3x^2 - 4x - 9

- 2x^3 + 2x^3 + 3x^2 - 3x^2 + 4x - 4x+ 5 - 9

=-4

This isn't a polynomial

Hence;

Option 3 answers the question

Answer from: Quest

answer: finding the extract measurements and knowing the points

step-by-step explanation:

Answer from: Quest

the length of o'p' is $1.5\times op$ .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

$k=\frac{o'p'}{op}$

the scale factor is 1.5.

$1.5=\frac{o'p'}{op}$

multiply both sides by op.

$1.5\times op=o'p'$

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is $1.5\times op$ .

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