List of top Mathematics Questions on Division of Algebraic Expressions Continued (Polynomial ÷ Polynomial)

Factorise the expressions and divide them as directed. 
  1. \((y^ 2 + 7y + 10) ÷ (y + 5)\) 
  2.  \((m^2 – 14m – 32) ÷ (m + 2)\) 
  3.  \((5p^ 2 – 25p + 20) ÷ (p – 1)\) 
  4.  \(4yz(z ^2 + 6z – 16) ÷ 2y(z + 8)\)
  5.  \(5pq(p^ 2 – q^ 2 ) ÷ 2p(p + q)\) 
  6.  \(12xy(9x^ 2 – 16y ^2 ) ÷ 4xy(3x + 4y)\) 
  7.  \(39y^ 3 (50y ^2 – 98) ÷ 26y ^2 (5y + 7)\)
Divide as directed. 
  1.  \(5(2x + 1) (3x + 5) ÷ (2x + 1) \)
  2.  \(26xy(x + 5)(y – 4) ÷ 13x(y – 4) \)
  3.  \(52pqr (p + q) (q + r) (r + p) ÷ 104pq(q + r) (r + p) \)
  4.  \(20(y + 4) (y^ 2 + 5y + 3) ÷ 5(y + 4) \)
  5.  \(x(x + 1) (x + 2) (x + 3) ÷ x(x + 1)\)
Work out the following divisions. 
  1. \((10x – 25) ÷ 5\) 
  2.  \((10x – 25) ÷ (2x – 5) \)
  3.  \(10y(6y + 21) ÷ 5(2y + 7) \)
  4.  \(9x^ 2 y^ 2 (3z – 24) ÷ 27xy(z – 8) \)
  5. \( 96abc(3a – 12) (5b – 30) ÷ 144(a – 4) (b – 6)\)
Divide the given polynomial by the given monomial. 
  1. \((5x^ 2 – 6x) ÷ 3x \)
  2. \( (3y^ 8 – 4y^ 6 + 5y ^4 ) ÷ y ^4 \)
  3.  \(8(x^ 3y^ 2 z^ 2 + x^ 2y ^3 z^ 2 + x^ 2y ^2 z ^3 ) ÷ 4x ^2y ^2 z ^2 \)
  4.  \((x^ 3 + 2x^ 2 +3x) ÷ 2x \)
  5.  \((p^ 3q^ 6 – p^ 6q ^3 ) ÷ p^ 3q ^3\)
Carry out the following divisions. 
  1. \(28x^ 4 ÷ 56x\) 
  2.  \(–36y^ 3 ÷ 9y ^2\) 
  3.  \(66pq^2 r^ 3 ÷ 11qr^2 \)
  4.  \(34x^ 3y^ 3 z^ 3 ÷ 51xy^2 z^ 3 \)
  5.  \(12a ^8b^ 8 ÷ (– 6a^ 6b ^4 )\)