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timurjin [86]
3 years ago
6

Complete the steps to factor the polynomial by grouping.P(x) = x3 + 5x2 – x – 5

Mathematics
2 answers:
ahrayia [7]3 years ago
6 0
<span>P(x) = x</span>³<span> + 5x</span>²<span> – x – 5

P(x) = x</span>²(x+5) - (x + 5)

P(x) = (x + 5)(x² - 1)

P(x) = (x + 5) (x + 1)(x -1)
valentina_108 [34]3 years ago
6 0

Answer

Find the  steps to factor the polynomial by grouping.

To prove

As given the polynomial in the question

P(x) = x³ + 5x² – x – 5

P(x) = x² (x + 5) – (x + 5)

Take  (x + 5) as common

P(x) =  (x + 5) (x² - 1)

As using the identity

(a² - b²) = (a - b)(a + b)

P(x) =  (x + 5) (x - 1)(x + 1)

Therefore the factors of the polynomial by grouping are (x + 5) and (x - 1)(x + 1) .

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Vanessa deposits $24,000 into each of two savings accounts. Account I earns 2. 4% interest compounded annually. Account II earns
ikadub [295]

The sum of the balances of these accounts at the end of 5 years is given by: Option B: $53,901.59 (approx)

<h3>How to calculate compound interest's amount?</h3>

If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:

CI = P(1 +\dfrac{R}{100})^T - P

The final amount becomes:

A = CI + P\\A = P(1 +\dfrac{R}{100})^T

<h3>How to calculate simple interest amount?</h3>

If the initial amount (also called as principal amount) is P, and the interest rate is R% annually, and it is left for T years for that simple interest, then the interest amount earned is given by:

I = \dfrac{P \times R \times T}{100}

For the considered case, we're given that:

  • Initial amount in both accounts deposited = $24,000 = P
  • Type of interest: Compound interest in first account and simple interest in second account
  • Unit of time: Annually
  • Rate of interest = 2.4% annually = R
  • Total unit of time for which amount is to be calculated: 5 years = T

In first account, the final amount at the end of 5 years is evaluated as:

A = 24000(1 + \dfrac{2.4}{100})^4 = 24000(1.024)^4  \approx 27021.59\: \rm (in \:  dollars)

In second account,  the final amount at the end of 5 years is evaluated as:

A = 24000 +  \dfrac{24000 \times 2.4 \times 5}{100} = 24000 + 2880 = 26880 \text{\: (in dollars)}

Total amount after 5 years in these accounts = 27021.59 + 26880 = 53901.59 (in dollars)

Thus, the sum of the balances of these accounts at the end of 5 years is given by: Option B: $53,901.59 (approx)

Learn more about compound interest here:

brainly.com/question/11897800

4 0
2 years ago
if the velocity of a body changes from 13m/s to 30m/s while undergoing constant acceleration whats the average velocity of the b
34kurt
Average speed = (1/2) (beginning speed + ending speed)
                          = (1/2)        ( 13 m/s  +  30 m/s )
                          =    (1/2)        ( 43 m/s )
                          =        21.5 m/s
3 0
3 years ago
Read 2 more answers
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