Question

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.  \(x(x + 1) (x + 2) (x + 3) ÷ x(x + 1)\)

Answer 1

(i) \(\frac{5(2x+1)(3x+5)}{(2x+1)}\)

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

---

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

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

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

---

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

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

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

---

(iv) \(20(y + 4) (y ^2 + 5y + 3) \)

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

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

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

= \(4(y^2+5y+3)\)

---

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

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

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