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Marat540 [252]
3 years ago
13

What is x^3−x^2−x+1 divided by x^2−2x+1 ?

Mathematics
2 answers:
Mars2501 [29]3 years ago
7 0

 

\displaystyle\bf\\x^3-x^2-x+1 = \\\\=x^2(x - 1) - (x - 1)= \\\\=(x - 1)(x^2 - 1) =\\\\= (x - 1)(x - 1)(x + 1) = \\\\=(x - 1)^2(x + 1) = \\\\(x^2 - 2x + 1)(x + 1)\\\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots\\(x^2 - 2x + 1)(x + 1)~\vdots~(x^2 - 2x + 1)\\\\\implies~~x^3-x^2-x+1~~\text{ is divisible by }~~ x^2-2x+1 \\\\Verify:\\\\\frac{x^3-x^2-x+1}{x^2-2x+1}=\frac{(x^2 - 2x + 1)(x + 1)}{x^2-2x+1}=x+1



shutvik [7]3 years ago
5 0
X^3-x^2-x+1 divided by x^2-2x+1 equals x + 1
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Which expression is equivalent to [(3xy^-5)^3 / (x^-2y^2)^-4]^-2
True [87]
<span>The answer is (x</span>¹⁰<span>y</span>¹⁴<span>)/729.

Explanation:
We can begin simplifying inside the innermost parentheses using the properties of exponents. The power of a power property says when you raise a power to a power, you multiply the exponents. This gives us

[(3</span>³<span>x</span>³<span>y</span>⁻¹⁵<span>)/(x</span>⁸<span>y</span>⁻⁸<span>)]</span>⁻²<span>.

Negative exponents tell us to "flip" sides of the fraction, so within the parentheses we have
[(3</span>³<span>x</span>³<span>y</span>⁸<span>)/(x</span>⁸<span>y</span>¹⁵<span>)]</span>⁻²<span>.

Using the quotient property, we subtract exponents when dividing powers, which gives us
(3</span>³<span>/x</span>⁵<span>y</span>⁷<span>)</span>⁻²<span>.

Evaluating 3</span>³<span>, we have
(27/x</span>⁵<span>y</span>⁷<span>)</span>⁻²<span>.

Using the power of a power property again, we have
27</span>⁻²<span>/x</span>⁻¹⁰<span>y</span>⁻¹⁴<span>.

Flipping the negative exponents again gives us x</span>¹⁰<span>y</span>¹⁴<span>/729.</span>
4 0
3 years ago
Read 2 more answers
Hello guysssssss asap
Vikentia [17]

Answer:

-9, -8, -4 , 6 then 9..

Step-by-step explanation:

Your welcome

8 0
3 years ago
How to find a unit rate 305 rotation in 5 minutes
wariber [46]
A unit rate will always end up having one as its denominator so divide 305 by 5 which is 61 rotations/1 minute.
3 0
4 years ago
6.Tanya bought a house for $270,000. She paid
nignag [31]

Answer:

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8 0
3 years ago
23 ones x 2 tens= answer
shutvik [7]
23 and 2 tens is 23 and 20 which equals 53

53
5 0
4 years ago
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