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Mathematics Question on Division of Algebraic Expressions Continued (Polynomial ÷ Polynomial)

Divide as directed.

  1. 5(2x+1)(3x+5)÷(2x+1)5(2x + 1) (3x + 5) ÷ (2x + 1)
  2. 26xy(x+5)(y–4)÷13x(y–4)26xy(x + 5)(y – 4) ÷ 13x(y – 4)
  3. 52pqr(p+q)(q+r)(r+p)÷104pq(q+r)(r+p)52pqr (p + q) (q + r) (r + p) ÷ 104pq(q + r) (r + p)
  4. 20(y+4)(y2+5y+3)÷5(y+4)20(y + 4) (y^ 2 + 5y + 3) ÷ 5(y + 4)
  5. x(x+1)(x+2)(x+3)÷x(x+1)x(x + 1) (x + 2) (x + 3) ÷ x(x + 1)
Answer

(i) 5(2x+1)(3x+5)(2x+1)\frac{5(2x+1)(3x+5)}{(2x+1)}

=5(3x+1)5(3x+1)

(ii) 26xy(x+5)(y−4)13x(y−4)\frac{26xy(x+5)(y-4)}{13x(y-4)}

=2×13×xy(x+5)(y−4)13x(y−4)\frac{2×13×xy(x+5)(y-4)}{13x(y-4)}

=2y(x+5)2y(x+5)

(iii) 52pqr(p+q)(q+r)(r+p)104pq(q+r)(r+p)\frac{52pqr (p + q) (q + r) (r + p)}{ 104pq (q + r) (r + p) }

= 2×2×13×p×q×r×(p+q)×(q+r)×(r+p)2×2×2×13×p×q×(q+r)×(r+p)\frac{2 × 2×13×p×q×r×(p+q)×(q+r)×(r+p)}{2×2×2×13×p×q×(q+r)×(r+p)}

=12r(p+q)\frac{1}{2}r(p+q)

(iv) 20(y+4)(y2+5y+3)20(y + 4) (y ^2 + 5y + 3)

= 2×2×5×(y+4)(y2+5y+3)2 × 2 × 5 × (y + 4) (y^ 2 + 5y + 3)

= 20(y+4)(y2+5y+3)5(y+4)\frac{20(y+4)(y^2+5y+3)}{5(y+4)}

= 2×2×5(y+4)×(y2+5y+3)5×(y+4)\frac{2× 2 × 5(y+4)×(y^2+5y+3)}{5×(y+4)}

= 4(y2+5y+3)4(y^2+5y+3)

(v)x(x+1)(x+2)(x+3)x(x+1)\frac{ x(x+1)(x+2)(x+3)}{x(x+1)}

=x(x+1)(x+2)(x+3)x(x+1)\frac{x(x+1)(x+2)(x+3)}{x(x+1)}

=(x+2)(x+3)(x+2)(x+3)