Factor the following expression completely given that one of the factors is (w − 7): w^3 − 12w^2 + 29w + 42 =

The factors of w^3 − 12w^2 + 29w + 42 are (w -7), (w-6) and (W + 1 )

Step-by-step explanation:

It is given that (w − 7) is one factor of w^3 − 12w^2 + 29w + 42

When we divide w^3 − 12w^2 + 29w + 42 by w-7 we get the quotient W^2 – 5w -6 and remainder 0

Therefore

w^3 − 12w^2 + 29w + 42 can be written as,

w^3 − 12w^2 + 29w + 42 = (w -7)(W^2 – 5w -6 )  

When we factorize W^2 – 5w -6 we get

W^2 – 5w -6 = (w+1)(w-6)

Therefore,

The factors of w^3 − 12w^2 + 29w + 42 are (w -7), (w-6) and (W + 1 )  

The long division method is attached  with this answer      

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation:

15%

step-by-step explanation:

use the table and count the number of guesses that has two correct answers.

the following are two correct answers

10010, 01100, 11000

a total of 3 numbers having 2 correct guesses out of 20 questions.

probability of getting 2 correct guesses = the number of questions getting 2 correct answers / total number of questions.

= 3/20

to convert it into percent multiply by 100, we get

= 3/20 * 100

= 15%

the answer is 15%

you.