Divide the polynomials. Your answer should be in the form p(x)+(k)/(x) where p is a polynomial and k is an integer. (3x^(3)-x-2)/(x)=

Identify dividend and divisor: Identify the dividend and the divisor. The dividend is the polynomial 3x^3 - x - 2, and the divisor is x.Divide each term by x: Divide each term of the polynomial by x. To divide a polynomial by x, divide each term of the polynomial by x individually. (3x^3 - x - 2) / x = (3x^3 / x) - (x / x) - (2 / x)Simplify each term: Simplify each term after division. 3x^3 / x = 3x^2 (since x^3 / x = x^(3-1) = x^2) x / x = 1 (since any non-zero number divided by itself is 1) 2 / x remains as it is because 2 is not divisible by x. So, (3x^3 - x - 2) / x = 3x^2 - 1 - (2 / x)Write final answer: Write the final answer in the required form. The polynomial part p(x) is 3x^2 - 1, and the integer k is -2. Therefore, the final answer is p(x) + (k / x) = 3x^2 - 1 - (2 / x).

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Math Problems

Algebra 1

Powers with decimal and fractional bases

Full solution

Q. Divide the polynomials.

\newline

Your answer should be in the form

p(x)+\frac{k}{x}

where

p

is a polynomial and

k

is an integer.

\newline

\frac{3 x^{3}-x-2}{x}=

Identify dividend and divisor: Identify the dividend and the divisor. The dividend is the polynomial $3x^3 - x - 2$ , and the divisor is $x$ .
Divide each term by x: Divide each term of the polynomial by x. $\newline$ To divide a polynomial by x, divide each term of the polynomial by x individually. $\newline$ $(3x^3 - x - 2) / x = (3x^3 / x) - (x / x) - (2 / x)$
Simplify each term: Simplify each term after division. $\newline$ $\frac{3x^3}{x} = 3x^2$ (since $\frac{x^3}{x} = x^{(3-1)} = x^2$ ) $\newline$ $\frac{x}{x} = 1$ (since any non-zero number divided by itself is $1$ ) $\newline$ $\frac{2}{x}$ remains as it is because $2$ is not divisible by $x$ . $\newline$ So, $\frac{(3x^3 - x - 2)}{x} = 3x^2 - 1 - \left(\frac{2}{x}\right)$
Write final answer: Write the final answer in the required form. $\newline$ The polynomial part $p(x)$ is $3x^2 - 1$ , and the integer $k$ is $-2$ . $\newline$ Therefore, the final answer is $p(x) + \frac{k}{x} = 3x^2 - 1 - \frac{2}{x}$ .