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Zinaida [17]
3 years ago
7

Which expression is equivalent to...? Screenshots attached, please help.

Mathematics
1 answer:
BaLLatris [955]3 years ago
3 0

For this case we must simplify the following expression:

\sqrt [3] {64 * a ^ 6 * b ^ 7 * c ^ 9}

We rewrite:

64 = 4 ^ 3\\a ^ 6 = (a ^ 2) ^ 3\\b ^ 6 * b = ((b ^ 2) ^ 3 * b)\\c ^ 9 = (c ^ 3) ^ 3

So:

\sqrt [3] {4 ^ 3 * (a ^ 2) ^ 3 * (b ^ 2) ^ 3 * b * (c ^ 3) ^ 3} =\\\sqrt [3] {4 * a ^ 2 * b ^ 2 * c ^ 3) ^ 3 * b} =

By definition of properties of powers and roots we have:

\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}

So:

4a ^ 2b ^ 2 c ^ 3 \sqrt [3] {b}

Answer:

Option B

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The factors of x cube -10x square -53x-42
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Answer:

<em><u></u></em>x^3 - 10 x^2 -53x -42 = ( x + 1)(x + 3) (x - 14)<em><u></u></em>

Step-by-step explanation:

 x^3 - 10x^2 -53x - 42

The factors of 42 : ±1 , ±2 , ±3 , ±6, ±7, ±14, ±21 , ±42

<u>Using trial and error method we will find the first root of the polynomial.</u>

1 : ( 1 )³ - 10 ( 1 )² - 53 ( 1 ) - 42

     1 - 10 - 53 - 42  ≠ 0

   Therefore 1 is not a root

-1 : ( -1 )³ - 10 (- 1 )² - 53 (- 1 ) - 42

      - 1 - 10 + 53 - 42

       53 - 53 = 0

Therefore - 1 is a root of the polynomial.

Therefore ( x + 1) is a factor.

<u>Now by long division or by using synthetic division we can find other factors.</u>

<u>Synthetic Division :</u>

                             -1 | 1      -10       -53      - 42

                                | 0     - 1          11          42

                                |______________________

                                  1      - 11       - 42        0

Therefore ,

x^3 - 10 x^2 -53x -42 = ( x + 1)(x^2 - 11x +42)  ------ ( 1 )

<u>Next further factorize x² - 11x - 42</u>

   x² - 11x - 42

= x² -  14x + 3x - 42

=x(x - 14) + 3 (x - 14)

=(x + 3 )(x - 14)

Therefore ,

x^3 - 10 x^2 -53x -42 = ( x + 1)(x + 3) (x - 14)

4 0
2 years ago
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