HELP ASAP. THIS IS DUE TONIGHT! What is the remainder when the polynomial p(x)= 5x^3 + x^2 + 10 is divided by (x + 2)?

Remainder theorem:

If you divide p(x) by (x-k), then the remainder is r = p(k)

Comparing x+2 to the form x-k, we see that k = -2

It might help to rewrite x+2 as x - (-2) to match the forms better.

Now plug this into the p(x) function getting...

p(x) = 5x^3 + x^2 + 10

p(k) = 5k^3 + k^2 + 10

p(-2) = 5(-2)^3 + (-2)^2 + 10

p(-2) = 5(-8) + 4 + 10

p(-2) = -40 + 4 + 10

p(-2) = -36+10

p(-2) = -26

The remainder is -26

You can use polynomial long division or synthetic division to confirm this.

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places

x = 2

step-by-step explanation:

if sr parallel to ba then the sides bc and ac are in proportion, that is

= ← substitute values

= ( cross- multiply )

27x = 6(4x + 1)

27x = 24x + 6 ( subtract 24x from both sides )

3x = 6 ( divide both sides by 3 )

x = 2