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3 years ago

Divide. If there is a remainder, express it in the form r x + 2 . ( x 3 − 4 x 2 − 4 x + 36 ) ÷ ( x + 2 )

Mathematics

1 answer:

mina [271]3 years ago

7 0

Answer:

Quotient= $x^2-6x+8$

Remainder= $\frac{20}{x+2}$

Step-by-step explanation:

We are given that an expression

$\frac{x^3-4x^2-4x+36}{x+2}$

We have to divide and express remainder in the form rx+2.

We have

Divisor: The polynomial which divides the dividend polynomial.

Dividend: The polynomial which is divided by the divisor.

Dividend= $x^3-4x^2-4x+36$

Divisor= $x+2$

Quotient: The polynomial which is obtained when the divisor divides the dividend.

Remainder: The polynomial which remains when the divisor divides the dividend.

Quotient= $x^2-6x+8$

Remainder= $\frac{20}{x+2}$

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Which polynomial correctly combines the like term and express the given polynomial in standard form

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Answer:

$8mn^5 - 2m^6 + 5m^2n^4 - m^3n^3 + n^6 - 4m^6 + 9m^2n^4 - mn^5 - 4m^3n^3 = -6m^6 - mn^5 - 5m^3n^3 + 14m^2n^4 + 8mn^5 + n^6$

Step-by-step explanation:

Given

$8mn^5 - 2m^6 + 5m^2n^4 - m^3n^3 + n^6 - 4m^6 + 9m^2n^4 - mn^5 - 4m^3n^3$

Required

Correctly combine the like terms

We have:

$8mn^5 - 2m^6 + 5m^2n^4 - m^3n^3 + n^6 - 4m^6 + 9m^2n^4 - mn^5 - 4m^3n^3$

Collect like terms (in decreasing degrees of m)

$- 2m^6 - 4m^6 - mn^5- m^3n^3 - 4m^3n^3+ 5m^2n^4 + 9m^2n^4 + 8mn^5 + n^6$

$-6m^6 - mn^5 - 5m^3n^3 + 14m^2n^4 + 8mn^5 + n^6$

So:

$8mn^5 - 2m^6 + 5m^2n^4 - m^3n^3 + n^6 - 4m^6 + 9m^2n^4 - mn^5 - 4m^3n^3 = -6m^6 - mn^5 - 5m^3n^3 + 14m^2n^4 + 8mn^5 + n^6$

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3 years ago

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Answer:

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Step-by-step explanation:

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Answer:

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3 years ago

Read 2 more answers

Type the correct answer in each box. write each answer as a fraction, using / for the fraction bar. wesley draws a card at rando

faust18 [17]

The probability that Wesley draws an ace or a jack is 0.154 and the probability that Wesley draws a number card or a black card is 0.846

<h3>The probability of Ace or jack</h3>

In a standard deck of cards, we have:

Total = 52

Ace = 4

Jack = 4

Ace and Jack = 0

The probability is then calculated as:

P = P(Ace) +P(Jack) - P(Ace and Jack)

This gives

P = 4/52 + 4/52 - 0/52

Evaluate

P = 0.154

Hence, the probability that Wesley draws an ace or a jack is 0.154

<h3>The probability of Number card or black card</h3>

In a standard deck of cards, we have:

Total = 52

Number card = 36

Black = 26

Number card and Black = 18

The probability is then calculated as:

P = P(Number card) +P(Black card) - P(Both)

This gives

P = 36/52 + 26/52 - 18/52

Evaluate

P = 0.846

Hence, the probability that Wesley draws a number card or a black card is 0.846