Polynomials and polynomial division
Extension: the degree and standard order of a polynomial, then dividing polynomials by filling a multiplication grid backwards, with a remainder and with missing powers.
- UK: Year 12
- Germany: grade 10
- Iran: grade 9
- Afghanistan: grade 9
- Syria: grade 11
- Palestine: grade 9
- Ukraine: grade 7
- Russia: grade 10
Guide
Extension: in the UK, dividing polynomials is A-level work. Iran and Afghanistan teach it in grade 9.
A polynomial is a sum of terms such as 2x2 − 3x + 5. Written in standard order, the powers go down. Its degree (of a polynomial) is the highest power of x, here 2; the coefficients are 2, −3 and 5.
Division is multiplication backwards. To divide x2 + 5x + 6 by x + 2, find the missing side of a rectangle: put x and 2 down the side of the grid and find the headings along the top, so the cells add up to x2 + 5x + 6.
Start with the highest power: x × ? = x², so the first heading is x. Fill its column, see what is still missing from the total, and repeat. The headings make the quotient.
If something is left that x + 2 cannot make, it is the remainder. Its degree is always lower than the divisor's.
Tap a heading or a cell, then type on the keypad.