Simplify the rational expression, $\frac { x ^ { 4 } + x ^ { 3 } - 21 x ^ { 2 } - 41 x - 20 } { x ^ { 2 } + 2 x + 1 }$ ,by using long division or synthetic division.
A) $x ^ { 2 } - x - 20$
B) $x ^ { 2 } - 9 x + 25$
C) $- x ^ { 2 } + 8 x + 25$
D) $x ^ { 2 } + 5 x + 4$
E) $- x ^ { 2 } + 9 x - 20$

Question

Simplify the rational expression, $\frac { x ^ { 4 } + x ^ { 3 } - 21 x ^ { 2 } - 41 x - 20 } { x ^ { 2 } + 2 x + 1 }$ ,by using long division or synthetic division. 
A) $x ^ { 2 } - x - 20$
B) $x ^ { 2 } - 9 x + 25$
C) $- x ^ { 2 } + 8 x + 25$
D) $x ^ { 2 } + 5 x + 4$
E) $- x ^ { 2 } + 9 x - 20$

Quizplus · Accepted Answer

The denominator $x^2 + 2x + 1$ factors to $(x + 1)^2$. Using long division or synthetic division to divide the numerator by the denominator, the quotient is $x^2 - x - 20$, which matches option A.

Simplify the Rational Expression x4+x3−21x2−41x−20x2+2x+1\frac { x ^ { 4 } + x ^ { 3 } - 21 x ^ { 2 } - 41 x - 20 } { x ^ { 2 } + 2 x + 1 }x2+2x+1x4+x3−21x2−41x−20​

Simplify the Rational Expression $\frac { x ^ { 4 } + x ^ { 3 } - 21 x ^ { 2 } - 41 x - 20 } { x ^ { 2 } + 2 x + 1 }$