DIVIDING POLYNOMIALS BY MONOMIALS

To divide a polynomial by a monomial, we can decompose the fraction into many fractions. Using the operations on exponents, we can simplify further.

Problem 1 :

9x2 - 3x + 123x

Solution :

9x2 - 3x + 123x= 9x23x - 3x3x + 123x= 3x - 1 + 4x

Problem 2 :

11x5 + 7x3 - 2xx2

Solution :

11x5 + 7x3 - 2xx2= 11x5x2 + 7x3x2 - 2xx2= 11x3 + 7x - 2x

Problem 3 :

8x3 - x2 + 2x - 12x

Solution :

8x3 - x2 + 2x - 12x= 8x32x - x22x + 2x 2x - 12x= 4x2 -x2 + 1 - 12x

Problem 4 :

x2 + 5x + 6x2

Solution :

x2+ 5x + 6x2= x2x2 + 5xx2 + 6x2= 1 + 5x + 6x2

Problem 5 :

x6 - 4x4 + 3x25x2

Solution :

x6- 4x4 + 3x25x2= x65x2 - 4x45x2 + 3x25x2= x45 - 4x25 + 35

Problem 6 :

x3 + 6x - 1-3x

Solution :

x3+ 6x -1-3x= x3-3x + 6x-3x - 1-3x= -x23 - 2 + 13x

Problem 7 :

3x5 - 15x3 + 6x9x

Solution :

3x5- 15x3 +6x9x= 3x59x - 15x39x + 6x 9x= x43 - 5x23 + 23

Problem 8 :

12x4y3z2w2xy2

Solution :

12x4y3z2w2xy2= 6x3yz2w

Problem 9 :

2a3b2 - 10ab3c2ab2

Solution :

2a3b2 - 10ab3c2ab2= 2a3b22ab2 - 10ab3c2ab2= a2 - 5bc

Problem 10 :

xy3z - 4y2z + 6xyz - y3z yz

Solution :

xy3z - 4y2z + 6xyz - y3z yz= xy3zyz - 4y2zyz + 6xyzyz - y3zyz= xy2 - 4y + 6x - y2

Problem 11 :

12y3z6y3

Solution :

12y3z6y3= 2z

Problem 12 :

6ab4c- 3a3bc2 + 2a3bc - 4ab3c abc

Solution :

6ab4c- 3a3bc2 + 2a3bc - 4ab3c abc= 6ab4cabc - 3a3bc2abc + 2a3bcabc - 4ab3cabc= 6b3 - 3a2c + 2a2- 4b2

Problem 13 :

2r2s3t + 2s3t2 + rs4t3s2t

Solution :

2r2s3t + 2s3t2 + rs4t3s2t= 2r2s3ts2t + 2s3t2s2t + rs4t3s2t= 2r2s + 2st + rs2t2

Problem 14 :

2ax3 + 4bx2x

Solution :

2ax3 + 4bx2x= 2ax32x + 4bx2x= ax2 + 2b

Problem 15 :

8uv + 10uv2w - 8uvw2uv

Solution :

8uv + 10uv2w - 8uvw2uv= 8uv2uv + 10uv2w2uv - 8uvw2uv= 4 + 5vw - 4w

Problem 16 :

4xyz + 12xyz2- 6xy2 + 12x3yz 2xy

Solution :

4xyz + 12xyz2- 6xy2 + 12x3yz 2xy= 4xyz2xy + 12xyz22xy - 6xy22xy + 12x3yz2xy= 2z + 6z2 - 3y + 6x2z

Problem 17 :

5ax2+ 15a3x5ax

Solution :

5ax2+ 15a3x5ax= 5ax25ax + 15a3x5ax= x + 3a2

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