Simplify the complete quantity of (x² - 15x + 56)/(x - 7)

Solution:

In the given problem, we need to simplify by factorising the given polynomial and then dividing with the expression given in the denominator.

Given:

Expression is (x² - 15x + 56)/(x - 7)

By splitting the middle term

= (x² - 7x - 8x + 56)/(x - 7)

Taking out the common terms

= [x(x - 7) - 8(x - 7)]/(x - 7)

By further simplification

= (x - 8)(x - 7)/(x - 7)

Cancelling x - 7 from both numerator and denominator, we get

= (x - 8)

Therefore, by simplification we get (x - 8).

Simplify the complete quantity of (x² - 15x + 56)/(x - 7)

Summary:

By simplification of the complete quantity of (x² - 15x + 56)/(x - 7) we get (x - 8).