Question

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

Answer 1

Answer: 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