Question

Write the five different pairs of dividends and divisors such that the quotient in each case is 2x.

Answer 1

The different pairs of dividends and divisors, such that quotient in each case is 2x, are:

(1) 4x⁴; 2x³ i.e. 4x⁴ ÷ 2x³
Dividend = 4x⁴ = 2 × 2 × x × x × x × x
Divisor = 2x³ = 2 × x × x× x
$\frac{4x^4}{2x^3}=\frac{\mathit{2}\mathit{\times }\mathit{2}\mathit{\times }\mathit{x}\mathit{\times }\mathit{x}\mathit{\times }\mathit{x}\mathit{\times }\mathit{x}}{\mathit{2}\mathit{\times }\mathit{x}\mathit{\times }\mathit{x}\mathit{\times }\mathit{x}}$
= 2x
∴ 4x⁴ ÷ 2x³ = 2x

(2) 32x²; 16x i.e. 32x² ÷ 16x
Dividend = 32x² = 2 × 2 × 2 × 2 × 2 × x × x
Divisor = 16x = 2 × 2 × 2 × 2× x
$\frac{32x^2}{16x}=\frac{2\times 2\times 2\times 2\times 2\times x\times x}{2\times 2\times 2\times 2\times x}$
= 2x
∴ 32x² ÷ 16 = 2x

(3) 34x⁶; 17x⁵ i.e. 34x⁶ ÷ 17x⁵
Dividend = 34x⁶ = 2 × 17 × x × x × x × x × x× x
Divisor = 17x⁵ = 17 × x× x × x × x× x
$\frac{34x^6}{17x^5}=\frac{2\times 17\times x\times x\times x\times x\times x\times x}{17\times x\times x\times x\times x\times x}$
= 2x
∴ 34x⁶ ÷ 17x⁵ = 2x

(4) 12x³; 6x² i.e. 12x³ ÷ 6x²
Dividend = 12x³ = 2 × 2 × 3× x × x × x
Divisor = 6x² = 2 × 3 × x × x
$\frac{12x^3}{6x^2}=\frac{2\times 2\times 3\times x\times x\times x}{2\times 3\times x\times x}$
= 2x
∴ 12x³ ÷ 6x² = 2x

(5) 38x⁷; 19x⁶ i.e. 38x⁷÷ 19x⁶
Dividend = 38x⁷ = 2 × 19 × x× x × x × x× x × x × x
Divisor = 19x⁶ = 19 × x × x× x × x × x× x
$\frac{38x^7}{19x^6}=\frac{2\times 19\times x\times x\times x\times x\times x\times x\times x}{19\times x\times x\times x\times x\times x\times x}$
= 2x
∴ 38x⁷ ÷ 19x⁶ = 2x