Dividing a monomial and a polynomial by a monomial
When dividing a monomial by a monomial, the coefficients are divided and the exponents of equal letters are subtracted: 45x⁵y³ : 9x²y = 5x³y². If the result is a monomial, the division is exact. To divide a polynomial by a monomial we divide each term of the polynomial by that monomial and add the results: (12m³n - 18m²n² + 6mn) : 6mn = 2m² - 3mn + 1. Check: the product of the quotient and the divisor must equal the dividend. A polynomial cannot always be divided exactly by a monomial: for example, dividing ab + ac by ab gives ac : ab = c : b, which is not a polynomial. In division we take only those values of the letters for which the divisor is not zero.
“Divide and check”: in pairs one pupil divides a monomial, the partner multiplies the quotient by the divisor to check. If the product equals the dividend, the pair scores.