Solve the equation (x − 1)(x + 2)( x+ 8)( x+ 5) = 19 with proper steps!!

x⁴ + 14x³ + 51x² + 14x - 99 = 0

Step-by-step explanation:

First and foremost, open the brackets by multiplying the variables out.

( x - 1 )( x + 2 ) and  ( x + 8 )( x + 5 ) = 19

Now ( x -  1 )( x + 2 ) = ( x × x + x × 2 -1 × x -1 x 2 )

                                = x² + 2x - x - 2

                                = x² + x - 2 (1)

Again, ( x + 8 )( x + 5 ) = ( x × x + x × 5 + 8 × x + 8 × 5 )

                                    = x² + 5x + 8x + 40

                                    = x² + 13x + 40 (2)

Now, Multiply  (1) and (2) and simplify hen equate the result to 19.

( x² + x - 2 )( x² + 13x + 40 )

( x²× x² + x² × 13x + x² × 40 )       =    x⁴ + 13x³ + 40x²

( x × x² + x × 13x + x × 40x )         =        +    x³  +  13x² + 40x

( -2 × x² -2 × 13x -2 × 40    )         =                    -    2x² -  26x - 80

                                                     =     x⁴ + 14x³ +   51x² + 14x - 80

Just carry out the arrangement as follow for easy understanding bearing in mind the powers .

We now equate the result with 19

x⁴ + 14x³ + 51x² + 14x - 80 = 19

x⁴ + 14x³ + 51x² + 14x - 80 - 19 = 0

x⁴ + 14x³ + 51x² + 14 x - 99 = 0

a.) list the factors of 40.

1/2/4/5/8/10/20/40

b.) list the factors of 40 that represent the number of cans that could be on each shelf.

5

c.) how many different arrangements of cans are possible?

just one because if you put more on one shelf you will go way over 40 and the cabinet will probably break.

d.) what are the possible arrangements of the cans?

put 5 cans on each self to reach 40 cans in total.

e.) which arrangement uses all the shelves?

5 because you can put 5 cans on each shelf, and since there are 8 shelfs you are equally going to get 40 cans.

5

step-by-step explanation: