Question

The expression $\left\lbrack \left( \frac{1 + \sqrt{4x + 1}}{2} \right)^{7}–\left( \frac{1–\sqrt{4x + 1}}{2} \right)^{7} \right\rbrack$is a polynomial in x of degree –

• A. 7
• B. 5
• C. 4
• D. 3

Answer 1

Answer: (D)

3

Answer 2

$\frac{1}{2^{7}.\sqrt{4x + 1}}$ $\left\lbrack \begin{aligned} & 2.\lbrack^{7}C_{1}\sqrt{4x + 1} +^{7}C_{3}(\sqrt{4x + 1})^{3} \\ & +^{7}C_{5}(\sqrt{4x + 1})^{5} +^{7}C_{7}(\sqrt{4x + 1})^{7}\rbrack \end{aligned} \right\rbrack$

=$\frac{1}{2^{6}}$ [⁷C₁ + ⁷C₃.(4x +1) + ⁷C₅ (4x + 1)² + ⁷C₇(4x + 1)³]

polynomial of degree = 3