The prodcut of two numbers is $16 x^{4} - 1$ .If one number is 2x-1,find the other.

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Solution

Product of two numbers = $16 x^{4} - 1$

One number=2x-1

Then second number = $\frac{16 x^{4} - 1}{2 x - 1} = 8 x^{3} + 4 x^{2} + 2 x + 1$

$8 x^{3} + 4 x^{2} + 2 x + 1 - ------------------- - 2 x - 1) 16 x^{4} - 1 (16 x^{4} - 8 x^{3} - + - --------------- - 8 x^{3} 8 x^{3} - 4 x^{2} - + - ----------- - 4 x^{2} 4 x^{2} - 2 x - + - ------- - 2 x - 1 2 x - 1 - + - ------- - \times - -------- -$

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