Worksheet on Dividing Polynomial by Monomial

Practice the questions given in the worksheet on dividing polynomial by monomial. The questions are based on dividing each term of the polynomial by the monomial and then simplify.

1. Divide a polynomial by a monomial:

(i) (m² – 2mn) ÷ m

(ii) (³ – 3z² + z) ÷ z

(iii) (k⁶ – 7k⁵ + 4k⁴) ÷ k²

(iv) (10y⁷ – 8y⁶ + 3y⁴) ÷ y³

(v) (15u⁵ – 25u⁴) ÷ (-5u³)

(vi) (27b⁶ – 36b⁵) ÷ 9b⁵

(vii) (-24c⁶ – 32c⁴) ÷ (-8c³)

(viii) (34m³n² – 51m²n³) ÷ 17mn

2. Simplify the following polynomial divided by monomial:

(i) 6x³ + 8x² + 4x by 2x

(ii) 4a³ + 20a² + 16a by 4a

(iii) 38m³ – 19m² + 57m by 19m

(iv) -5z⁶ + 6z⁴ + z² + 4 by 2z²

(v) 10m²n – 15mn – 25mn² by (-2/5)mn

(vi) 21a³b³ + 35a⁴b² – 56a²b⁴ by -7a²b²

3. Divide the following polynomial by monomial and write the answer in simplest form:

(i) 7x³ – 35x² + 49x by 7x

(ii) 18u²v² – 3uv² + 9uv³ by 3uv

(iii) 8m²n – 5mn² – 20mn by (1/4)mn

(iv) a⁴ - 3a³ + (1/2)a² by 3a

(v) –t⁴ + t² by √3t²

Answers for the worksheet on dividing polynomial by monomial are given below to check the exact answers of the above questions on division of a polynomial by a monomial.

Answers:

1. (i) m – 2n

(ii) z² - 3z + 1

(iii) k⁴ – 7k³ + 4k²

(iv) 10y⁴ – 8y³ + 3y

(v) 3u² + 5u

(vi) 3b – 4

(vii) 3c³ + 4c

(viii) 2m²n – 3mn²



2. (i) 3x² + 4x + 2

(ii) a² + 5ac + 4

(iii) 2m² – m + 3

(iv) (-5/2)z⁴ + 3z² + 1/2 + 2/z²

(v) -25m + (125/2)n + 75/2

(vi) -5a² - 3ab + 8b²



3. (i) x² – 5x + 7

(ii) 6uv – v + 3v²

(iii) 32m - 20n - 80

(iv) a³/3 – a² + (1/6)a

(v) –t²/√3 + 1/√3

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