Answer: x-1
Step-by-step explanation: if the area of a rectangle is the length multiplied by the width, the width would be the area divided by the length:
A=L*W
W=A/L
substituting the given expressions:
[tex]W=\frac{x^{4}+4x^{3}+3x^{2}-4x-4 }{x^{3} +5x^{2}+8x+4 }[/tex]
now dividing the polynomials we have that the first term of the quotient is given by:
[tex]\frac{x^{4} }{x^{3} } =x[/tex]
when multiplying this term by the divisor and substracting the result from the dividend we are left with the following polynomial:
[tex]-x^{3}-5x^{2}-8x-4[/tex]
the second term of the quotient is given by:
[tex]\frac{-x^{3} }{x^{3} } =-1[/tex]
when multiplying by the divisor and substracting it from the divident the remainder is zero.
so the answer is W=x-1
