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3 years ago

How to solve this problem (x^n+y^n) divisible by (x+y)

1 answer:

8 0

$Use \\\\a^n + b^n = (a+b)(a^{n-1}b^0 - a^{n-2}b^1 + a^{n-3}b^2 - ... - a^1b^{n-2} + a^0b^{n-1}) \\--------------------------------\\\\\dfrac{x^n+y^n}{x+y}=\dfrac{(x+y)(x^{n-1}y^0-x^{n-2}y^1+x^{n-3}y^2-...-x^1y^{n-2}+x^0y^{n-1})}{x+y}\\\\=\boxed{x^{n-1}-x^{n-2}y+x^{n-3}y^2-...-xy^{n-2}+y^{n-1}}$

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Long division<br> 3x+1/6x^6+5x^5+2x^4-9x^3+7x^2-10x+2

inna [77]

$(6 x^{6}+5x^{5}+2x^{4}-9x^{3}+7x^{2}-10x+2) / (3x+1)$

We divide first number from first parenthesis with first number from second parenthesis. Then the resulting number we multiply by all numbers in second parenthesis and substract from first parenthesis.

$6 x^{6}/3x = 2 x^{5} \\ \\ 6 x^{6}+5x^{5}+2x^{4}-9x^{3}+7x^{2}-10x+2 - 6 x^{6} -2 x^{5} = 3x^{5}+2x^{4}-9x^{3}+7x^{2}-10x+2\\$

We repeat previous steps until we run out of numbers:
$3x^{5}/3x=x^{4} \\ \\ 3x^{5}+2x^{4}-9x^{3}+7x^{2}-10x+2-3x^{5}-x^{4}= \\ \\ x^{4}-9x^{3}+7x^{2}-10x+2 \\ \\ \\ x^{4}/3x= \frac{1}{3} x^{3} \\ \\ x^{4}-9x^{3}+7x^{2}-10x+2-x^{4}- \frac{1}{3} x^{3}= \\ \\ - \frac{28}{3} x^{3}+7x^{2}-10x+2 \\ \\ \\ - \frac{28}{3} x^{3}/3x= - \frac{28}{9} x^{2} \\ \\ - \frac{28}{3} x^{3}+7x^{2}-10x+2+ \frac{28}{3} x^{3}+ \frac{28}{9} x^{2} = \\ \\ \frac{91}{9} x^{2}-10x+2$
$\frac{91}{9} x^{2}/3x=\frac{91}{27} x \\ \\ \frac{91}{9} x^{2}-10x+2-\frac{91}{9} x^{2}-\frac{91}{27} x= \\ \\ -\frac{361}{27} x+2 \\ \\ \\ -\frac{361}{27} x/3x=-\frac{361}{81} \\ \\ -\frac{361}{27} x+2+\frac{361}{27}x+\frac{361}{27}= \\ \\ \frac{415}{27}$

We are left with a number that has no x inside. This is remainder.
The final solution is sum of all these solutions and remainder:
$(2 x^{5}+x^{4}+\frac{1}{3} x^{3} - \frac{28}{9} x^{2} +\frac{91}{27} x)+(-\frac{361}{81} )$

6 0

3 years ago

What is -2(x+1) simplified

IrinaVladis [17]

Answer:

-2x - 2

Step-by-step explanation:

-2(x + 1)

$(-2)(x+1)$
$(-2)(x)+(-2)(1)$
$-2x - 2$

Therefore, the answer is -2x - 2.

8 0

3 years ago

A4(3a2 - 2a + 1)<br> What’s the product

guajiro [1.7K]

The answer is

3a^6 - 2a^5 + a^4

6 0

2 years ago

Monthly earnings total $4513. Find the social security tax deducted.

levacccp [35]

<span>The monthly earning is = 4513 dollars.
Find the security tax.
in US, 3% is the security tax.
3% = 3% / 100 = 0.03
NOw, let's solve with this given digits.
=> 4513 * .03 = 135.39
=> 135.39
Therefore the tax deducted to your salary is 135.39 dollars per month.

</span>

4 0

3 years ago

If f(x)= 3x + 10x and g(x)=5x - 3 find (f+g)(x)

Illusion [34]

Answer:

18x-3

Step-by-step explanation:

f(x)= 3x + 10x

g(x)=5x - 3

f(x)+g(x) = 3x + 10x + 5x - 3

Combine like terms

= 18x -3

6 0

3 years ago