Write the quadratic equation in factored form. be sure to write the entire equation. x2 - 5x - 24 = 0

x² - 5x - 24 = 0

First, we have to solve the quadratic equation and find the two values of x that fit the equation.

There are two values of x that fit:

x₁ = (5+11)/2 = 16/2 = 8

x₂ = (5-11)/2 = -6/2 = -3

Now I can restate the original equation in terms of a product of factors, with this product being equal to zero:

(x - x₁) * (x - x₂) = 0

ANSWER (x-8) * (x+3) = 0

Now I can solve each factor by setting each one equal to zero and solving the resulting linear equations:

x - 8 = 0 or x + 3 = 0

x = 8 or x = -3

We can check that these two values are the solution to the original quadratic equation.

x² - 5x - 24 = 0

First value

8² -5*8 -24 = 0

64 - 40 -24 = 0

0 = 0 ¡Checked!

Second value

(-3)² -5(-3) -24 = 0

9 + 15 -24 = 0

0 = 0 ¡Checked!

Hope this helps!

step-by-step explanation:

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for