Question

x⁴+ x² + 6÷x - 1. Divide and verify the result​

Answer 1

Step-by-step explanation:

for verification do (x³+x²+2x+2)×(x-1) + 8

Answer 2

Answer:

x³ + x² + 2x + 2 + $\frac{8}{x-1}$

Step-by-step explanation:

( $x^{4}$ + x² + 6 ) ÷ ( x - 1 ) = x³ + x² + 2x + 2 + $\frac{8}{x-1}$

Verification:

( x³ + x² + 2x + 2 + $\frac{8}{x-1}$ ) × ( x - 1 ) =

= x³ ( x - 1 ) + x² ( x - 1 ) + 2x (x - 1 ) + 2 ( x - 1 ) + $\frac{8}{x-1}$ ( x - 1 ) =

= $x^{4}$ - x³ + x³ - x² + 2x² - 2x + 2x - 2 + 8 = $x^{4}$ + x² + 6