Question

8x2 − 5 + 7x4 − 9x − x5

Answer 1

Answer:

$=-\left(x-1\right)\left(x^4-6x^3-6x^2-14x-5\right)$

Step-by-step explanation:

Factor out comon Term -1

$=-\left(x^5-7x^4-8x^2+9x+5\right)$

Factor $x^5-7x^4-8x^2+9x+5:\quad \left(x-1\right)\left(x^4-6x^3-6x^2-14x-5\right)$

$x^5-7x^4-8x^2+9x+5$

Use the rational root theorem

$a_0=5,\:\quad a_n=1$

The dividers of $a_{0}$: 1, 5, The dividers of $a_n$: 1

Therefore, check the following rational numbers: ±$\frac{1,\:5}{1}$

$\frac{1}{1}$ is a root of the expression, so factor out $x-1$

$=\left(x-1\right)\frac{x^5-7x^4-8x^2+9x+5}{x-1}$

$\frac{x^5-7x^4-8x^2+9x+5}{x-1}=x^4-6x^3-6x^2-14x-5$

$=x^4-6x^3-6x^2-14x-5$

$=-\left(x-1\right)\left(x^4-6x^3-6x^2-14x-5\right)$