Answer:
x³ − 5x + 3
Step-by-step explanation:
To solve with long division:
Start by dividing the highest terms:
x⁵ / x² = x³
This becomes the first term of the quotient. Multiply by the divisor:
x³ (x² + 2x + 5) = x⁵ + 2x⁴ + 5x³
Subtract from the first three terms of dividend:
(x⁵ + 2x⁴ + 0x³) − (x⁵ + 2x⁴ + 5x³) = -5x³
Drop down the next two terms and repeat the process.
To use the "box" method:
Each square in the box is the product of the term at the top of the column and the term at the end of the row. Also, squares diagonal of each other must add up to the term outside the box.
Look at the first diagonal. There is only one square, so that must be x⁵. Knowing this, we can say that x³ must be at the top of the column. We can fill in the rest of the column (2x⁴ and 5x³).
Repeat this process until all squares are filled in.
