The other factor represented by ? so that (x - 7)(x² - 16) = x³ - 7x² - 16x + 112 is ? = (x² - 16)
Applying the long division method will require us to; divide, multiply, subtract, bring down the next number and repeat the process to end at zero or arrive at a remainder.
We shall divide the expression x³ - 7x² - 16x + 112 by x - 7 as follows;
x³ divided by x equals x²
x - 7 multiplied by x² equals x³ - 7x²
subtract x³ - 7x² from x³ - 7x² - 16x + 112 will result to -16x + 112
-16x divided by x equals -16
x - 7 multiplied by -16 equals -16x + 112
subtract -16x + 112 from -16x + 112 will result to zero (0).
(x - 7)(x² - 16) = x³ - 7x² - 16x + 112
Therefore by the long division method, x³ - 7x² - 16x + 112 divided by x - 7 gives the other factor of (x² - 16).
Complete question:
What is the expression represented by ? so that (x - 7)(x² - 16) = x³ - 7x² - 16x + 112?