Find if (-2x-5) is a factor of the polynomial p(x) = 3x⁴ + 5x³ - 2x² - 4 or not.

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Question

Find if (-2x-5) is a factor of the polynomial p(x) =
3x4 + 5x3 - 2x2 - 4 or not

Ajanta Trivedi · Accepted Answer

the given polynomial is $p (x) = 3 x^{4} + 5 x^{3} - 2 x^{2} - 4$

put $- 2 x - 5 = 0 \Rightarrow x = - \frac{5}{2}$

therefore we will calculate $p (- \frac{5}{2})$

$p (- \frac{5}{2}) = 3 * (- \frac{5}{2})^{4} + 5 * (- \frac{5}{2})^{3} - 2 * (- \frac{5}{2})^{2} - 4 = 3 * \frac{625}{16} - 5 * \frac{125}{8} - 2 * \frac{25}{4} - 4 = \frac{625 (3 - 10)}{16} - \frac{25}{2} - 4 = \frac{- 625 * 7}{16} - \frac{25 + 8}{2} < 0$

therefore $p (- \frac{5}{2}) \neq 0$ thus (-2x-5) is not the factor of p(x).

hope this helps you.

cheers!!

Find if (-2x-5) is a factor of the polynomial p(x) = 3x4 + 5x3 - 2x2 - 4 or not.

Find if (-2x-5) is a factor of the polynomial p(x) = 3x⁴ + 5x³ - 2x² - 4 or not.