Dividing polynomials
(x³ + 8x² + 10x − 12) ÷ (x + 6)
Divide: (x³ + 8x² + 10x − 12) ÷ (x + 6)
(x³ + 8x² + 10x − 12) ÷ (x + 6)
- A polynomial goes into the house the same way a number does, and long division starts at the LEFT. Every term sits in its own column, and that is what makes the subtractions line up.
- x³ ÷ x is x², so x² goes in the x² place. Multiply the whole divisor by it — x²(x + 6) is x³ + 6x² — and take that away, leaving 2x² + 10x − 12.
- 2x² ÷ x is 2x, so 2x goes in the x place. Multiply the whole divisor by it — 2x(x + 6) is 2x² + 12x — and take that away, leaving −2x − 12.
- −2x ÷ x is −2, so −2 goes in the constant place. Multiply the whole divisor by it — −2(x + 6) is −2x − 12 — and take that away, leaving 0.
- Nothing is left, so x + 6 divides it exactly: (x³ + 8x² + 10x − 12) ÷ (x + 6) = x² + 2x − 2.
How it works.
- 01
A polynomial goes into the house the same way a number does, and long division starts at the LEFT. Every term sits in its own column, and that is what makes the subtractions line up.
- 02
x³ ÷ x is x², so x² goes in the x² place. Multiply the whole divisor by it — x²(x + 6) is x³ + 6x² — and take that away, leaving 2x² + 10x − 12.
- 03
2x² ÷ x is 2x, so 2x goes in the x place. Multiply the whole divisor by it — 2x(x + 6) is 2x² + 12x — and take that away, leaving −2x − 12.
- 04
−2x ÷ x is −2, so −2 goes in the constant place. Multiply the whole divisor by it — −2(x + 6) is −2x − 12 — and take that away, leaving 0.
- 05
Nothing is left, so x + 6 divides it exactly: (x³ + 8x² + 10x − 12) ÷ (x + 6) = x² + 2x − 2.