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) (m
^{2} – 2mn) ÷ m
(ii) (
^{3} – 3z
^{2} + z) ÷ z
(iii) (k
^{6} – 7k
^{5} + 4k
^{4}) ÷ k
^{2}
(iv) (10y
^{7} – 8y
^{6} + 3y
^{4}) ÷ y
^{3}
(v) (15u
^{5} – 25u
^{4}) ÷ (-5u
^{3})
(vi) (27b
^{6} – 36b
^{5}) ÷ 9b
^{5}
(vii) (-24c
^{6} – 32c
^{4}) ÷ (-8c
^{3})
(viii) (34m
^{3}n
^{2} – 51m
^{2}n
^{3}) ÷ 17mn
2. Simplify the following
polynomial divided by monomial:
(i) 6x
^{3} + 8x
^{2} + 4x by 2x
(ii) 4a
^{3} + 20a
^{2} + 16a by 4a
(iii) 38m
^{3} – 19m
^{2} + 57m by 19m
(iv) -5z
^{6} + 6z
^{4} + z
^{2} + 4 by 2z
^{2}
(v) 10m
^{2}n – 15mn – 25mn
^{2} by (-2/5)mn
(vi) 21a
^{3}b
^{3} + 35a
^{4}b
^{2} – 56a
^{2}b
^{4} by -7a
^{2}b
^{2}
3. Divide the following polynomial by monomial
and write the answer in simplest form:
(i) 7x
^{3} – 35x
^{2} + 49x by 7x
(ii) 18u
^{2}v
^{2} – 3uv
^{2} + 9uv
^{3} by 3uv
(iii) 8m
^{2}n – 5mn
^{2} – 20mn by (1/4)mn
(iv) a
^{4} - 3a
^{3} + (1/2)a
^{2} by 3a
(v) –t
^{4} + t
^{2} by √3t
^{2}
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) z
^{2} - 3z + 1
(iii) k
^{4} – 7k
^{3} + 4k
^{2}
(iv) 10y
^{4} – 8y
^{3} + 3y
(v) 3u
^{2} + 5u
(vi) 3b – 4
(vii) 3c
^{3} + 4c
(viii) 2m
^{2}n – 3mn
^{2}
2. (i) 3x
^{2} + 4x + 2
(ii) a
^{2} + 5ac + 4
(iii) 2m
^{2} – m + 3
(iv) (-5/2)z
^{4} + 3z
^{2} + 1/2 + 2/z
^{2}
(v) -25m + (125/2)n + 75/2
(vi) -5a
^{2} - 3ab + 8b
^{2}
3. (i) x
^{2} – 5x + 7
(ii) 6uv – v + 3v
^{2}
(iii) 32m - 20n - 80
(iv) a
^{3}/3 – a
^{2} + (1/6)a
(v) –t
^{2}/√3 + 1/√3
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