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nignag [31]
2 years ago
6

Use the Factor Theorem to show that (x - 3) is a factor of the polynomial

Mathematics
1 answer:
Katyanochek1 [597]2 years ago
7 0

Answer:

<em>P(3) = 0</em>

Step-by-step explanation:

<u>Factor Theorem is a consequence of Remainder Theorem. </u>

Remainder Theorem states that if polynomial f(x) is divided by a binomial (x - a) then the remainder is f(a).

Factor Theorem states that if f(a) = 0, then the binomial (x - a) is a factor of f(x).

We have the polynomial

P(x) = x^5-3x^4+5x^3-15x^2-6x+18

To prove that x-3 is a factor of P, we calculate P(3):

P(3) = 3^5-3*3^4+5*3^3-15*3^2-6*3+18

P(3) = 243-243+135-135-18+18

P(3) = 0

Thus, x-3 is a factor of P(x)

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How do you find the percent of a number?
Tom [10]

Answer:

(hope this helps can i plz have brainlist :D hehe)

Step-by-step explanation:

How to Calculate Percentages

There are many formulas for percentage problems. You can think of the most basic as X/Y = P x 100. The formulas below are all mathematical variations of this formula.

Let's explore the three basic percentage problems. X and Y are numbers and P is the percentage:

Find P percent of X

Find what percent of X is Y

Find X if P percent of it is Y

Read on to learn more about how to figure percentages.

1. How to calculate percentage of a number. Use the percentage formula: P% * X = Y

Example: What is 10% of 150?

Convert the problem to an equation using the percentage formula: P% * X = Y

P is 10%, X is 150, so the equation is 10% * 150 = Y

Convert 10% to a decimal by removing the percent sign and dividing by 100: 10/100 = 0.10

Substitute 0.10 for 10% in the equation: 10% * 150 = Y becomes 0.10 * 150 = Y

Do the math: 0.10 * 150 = 15

Y = 15

So 10% of 150 is 15

Double check your answer with the original question: What is 10% of 150? Multiply 0.10 * 150 = 15

2. How to find what percent of X is Y. Use the percentage formula: Y/X = P%

Example: What percent of 60 is 12?

Convert the problem to an equation using the percentage formula: Y/X = P%

X is 60, Y is 12, so the equation is 12/60 = P%

Do the math: 12/60 = 0.20

Important! The result will always be in decimal form, not percentage form. You need to multiply the result by 100 to get the percentage.

Converting 0.20 to a percent: 0.20 * 100 = 20%

So 20% of 60 is 12.

Double check your answer with the original question: What percent of 60 is 12? 12/60 = 0.20, and multiplying by 100 to get percentage, 0.20 * 100 = 20%

3. How to find X if P percent of it is Y. Use the percentage formula Y/P% = X

Example: 25 is 20% of what number?

Convert the problem to an equation using the percentage formula: Y/P% = X

Y is 25, P% is 20, so the equation is 25/20% = X

Convert the percentage to a decimal by dividing by 100.

Converting 20% to a decimal: 20/100 = 0.20

Substitute 0.20 for 20% in the equation: 25/0.20 = X

Do the math: 25/0.20 = X

X = 125

So 25 is 20% of 125

Double check your answer with the original question: 25 is 20% of what number? 25/0.20 = 125

Remember: How to convert a percentage to a decimal

Remove the percentage sign and divide by 100

15.6% = 15.6/100 = 0.156

Remember: How to convert a decimal to a percentage

Multiply by 100 and add a percentage sign

0.876 = 0.876 * 100 = 87.6%

(hope this helps can i plz have brainlist :D hehe)

4 0
2 years ago
Read 2 more answers
16% of what cookies is 44 cookies
Vsevolod [243]
275??
16×=4400

16×/16=4400/16
x=275
5 0
3 years ago
Mrs. Brown drove 105 miles in 2.5 hours. What was Mrs. Browns speed in miles per hour?
fiasKO [112]

Answer:

42mph.

Step-by-step explanation:

We know that the formula for miles per hour is.

r = d/t

R is our rate or miles per hour.

D is our distance.

T is our time.

In this case our distance is 105 miles.

And our times is 2.5 hours.

Therefore if we substitute them into our formula:

105mi ÷ 2.5hrs = 42mph

Hope this helped!

8 0
2 years ago
Help help (12 points)
iren2701 [21]

Answer:

2m+2m

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
What is the cosine if the sine=√5÷6
qwelly [4]

Answer:

cosine =  √31/6

Step-by-step explanation:

It is given that,

sine=√5/6

we know that, sine = opposite side/Hypotenuse

<u>To find Adjacent side</u>

Adjacent side = √(Hypotenuse² - opposite side²)

Adjacent side =√(6² - √5² ) = √(36 - 5 ) = √31

<u>To find cosine</u>

cosine = Adjacent side/Hypotenuse

cosine =  √31/6

7 0
3 years ago
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