List of top Mathematics Questions on Polynomials asked in JEE Main

\( f(x) \) is a 5 degree polynomial that has extremes at \( x = \pm 1 \) and \( \lim_{x \to 0} \frac{f(x)}{x^3} = 5 \), then \( f(2) - f(-2) \) is:
Let \( \alpha_1, \alpha_2, \dots, \alpha_7 \) be the roots of the equation \( x^7 + 3x^5 - 13x^3 - 15x = 0 \) and \( |\alpha_1| \geq |\alpha_2| \geq \dots \geq |\alpha_7| \). Then \( \alpha_1 \alpha_2 - \alpha_3 \alpha_4 + \alpha_5 \alpha_6 \) is equal to:
Let \(α_1,α_2,….,α_7\) be the roots of the equation \(𝑥^7+3𝑥^5−13𝑥^3−15𝑥=0\) and \(|α_1|≥|α_2|≥⋯≥ |α_7|\). Then \(α_1α_2−α_3α_4+α_5α_6\) is equal to ____.
Let \( f(x) \) be a polynomial of degree 6 in \( x \), in which the coefficient of \( x^6 \) is unity and it has extrema at \( x = -1 \) and \( x = 1 \). If \( \displaystyle \lim_{x \to 0} \frac{f(x)}{x^3} = 1 \), then \( 5 \cdot f(2) \) is equal to __________.
If f(x) and g(x) are two polynomials such that the polynomial P(x) = f(x³) + x · g(x³) is divisible by x² + x + 1, then P(1) is equal to ________.
The number of real solution x|x + 5| + 2|x + 7| - 2 = 0 is
\(\left( \frac{3^{\frac{1}{5}}}{x}+\frac{2x}{5^\frac{1}{3}} \right)^{12}\)Find which term is constant.