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) $\frac{5(2x+1)(3x+5)}{(2x+1)}$

=$5(3x+1)$

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

=$\frac{2×13×xy(x+5)(y-4)}{13x(y-4)}$

=$2y(x+5)$

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

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

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

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(iv) $20(y + 4) (y ^2 + 5y + 3)$

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

= $\frac{20(y+4)(y^2+5y+3)}{5(y+4)}$

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

= $4(y^2+5y+3)$

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

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

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