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kirill115 [55]
2 years ago
11

X^3 + 5x^2 - 8x^2 - 40x + 7x + 35

Mathematics
1 answer:
Temka [501]2 years ago
3 0

Remark

x - 1 is a root.

Proof

x - 1 = 0

x =  1

(1)^3 + 5(1)^2 - 8(1)^2 - 40(1) + 7(1) + 35

1 + 5 - 8 - 40 + 7 + 35

6 + 7 + 35 - 48 = 0

Solution

Divide x - 1 into the original equation.

x^3 + 5x^2 - 8x^2 - 33x + 35

x - 1 || x^3 - 3x^2  - 33x + 35  || x^2 - 2x  - 35

         <u>x^3 -  x^2</u>

                  -2x^2 - 33x

                   <u>-2x^2 + 2x</u>

                             - 35x + 35

                             <u>-35x + 35</u>

                                       0

x^2 - 2x - 35 factors into (x - 7)(x + 5)

Complete factorization

(x - 1)(x - 7)(x + 5)    

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The index of the refraction is 0.898 and the index of the refraction is less than one which is unreasonable because the speed of the light can't be more than c.

<h3>What is refraction?</h3>

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Learn more about the refraction here:

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