The projected population in thousands for a city over the next several years can be estimated by the function P(x)= x^3 + 2x^2 - 8x + 520, where x is the number of years since 2005. Use synthetic substitution to estimate the population.

Question

The projected population in thousands for a city over the next several years can be estimated by the function P(x)= x^3 + 2x^2 - 8x + 520, where x is the number of years since 2005. Use synthetic substitution to estimate the population.

Also could anyone help me with the difference of squares for example 18x^3+9x^2-2x-1;2x+1. once i divide out the 2 i don't know what to do with the fractions.

Answer 1

This is after 7 years and may not be able to help you Alexus anymore, but could help someone in the future :D

Send me ''hi ...'' to mathelper06
I don't really know how to write the answer and explanation on here (on the computer), so I would rather like to send my work with an explanation written on paper! Thanks!

Answer 2

lmao wait i meant mathelper06 sorrryyyy

Answer 3

this website aint lettin me write my email so just y'all know I'm using g m a i l lol'

Answer 4

Im from the future answer is 2

Answer 5

To estimate the population using synthetic substitution, we need to substitute a value for x into the function P(x) and then evaluate the expression. In this case, x represents the number of years since 2005.

Let's say we want to estimate the population for the year 2010. To do this, we need to calculate the value of x for that year. Since x represents the number of years since 2005, for the year 2010, x would be 2010 - 2005 = 5.

Now we can use synthetic substitution to estimate the population for the year 2010.

Step 1: Write the coefficients of the terms in the polynomial function in the form of an array. For P(x) = x^3 + 2x^2 - 8x + 520, the array representation of the coefficients is [1, 2, -8, 520].

Step 2: Start with the first coefficient (1) and write it in the synthetic division array.

1 | 1 2 -8 520
Where the numbers below the line represent the coefficients of the polynomial.

Step 3: Bring down the first coefficient (1).

1 | 1 2 -8 520
1

Step 4: Multiply the value you brought down (1) by the value of x (5), and write the result underneath the next coefficient (-8). Add the two numbers together.

1 | 1 2 -8 520
1
---
1

1 | 1 2 -8 520
1 5
---
1 7

Step 5: Repeat the process, multiplying the result (7) by the value of x (5) and adding it to the next coefficient (520).

1 | 1 2 -8 520
1 5 70
---
1 7 62

The final number in the last row, 62, is the remainder.

Therefore, when x = 5 (representing the year 2010), the estimated population, according to the function P(x), is 62,000.

Now, let's move on to the difference of squares.

For the given expression, 18x^3 + 9x^2 - 2x - 1, it doesn't seem to be a difference of squares. However, if you want to simplify it further by factoring, here's how you can do it:

Step 1: Group the terms separately.

(18x^3 + 9x^2) + (-2x - 1)

Step 2: Factor out the greatest common factor from each group.

9x^2(2x + 1) - 1(2x + 1)

Step 3: Notice that we have a common binomial factor, (2x + 1), in both terms.

(2x + 1)(9x^2 - 1)

Now, the expression is factored as (2x + 1)(9x^2 - 1).

Answer 6

18x^3+9x^2 - (2x+1)

9x^2(2x+1) - (2x+1)
(9x^2-1)(2x+1)
(3x+1)(3x-1)(2x+1)