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
