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Express (4x3 + 5x + 1)/(x2 + 1) using long division method in the form q(x) + r(x)/b(x) where q(x) is the quotient, r(x) is the remainder, and b(x) is the divisor.

Express 4x3 5x 1x2 1 using long division method in the form qx rxbx where qx is the quotient rx is the remainder and bx is the divisor class=

Respuesta :

Answer:

4x + (x + 1) / (x^2 + 1)

Explanation:

We perform the long division

The result of the above long division tells is that

[tex]4x^3+5x+1=4x(x^2+1)+(x+1)[/tex]

If we now divide both sides by x^2 + 1, we get

[tex]\frac{4x^3+5x+1}{x^2+1}=\frac{4x(x^2+1)+(x+1)}{x^2+1}[/tex][tex]=\frac{4x(x^2+1)}{x^2+1}+\frac{(x+1)}{x^2+1}[/tex][tex]=4x+\frac{x+1}{x^2+1}[/tex]

Hence,

[tex]\boxed{\frac{4x^3+5x+1}{x^2+1}=4x+\frac{x+1}{x^2+1}\text{.}}[/tex]

Therefore, the first choice from the options is the correct answer!

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