Divide the polynomials. The form of your answer should either be p(x) or p(x)+(k)/(x-3) where p(x) is a polynomial and k is an integer. (x^(3)-4x-15)/(x-3)=◻

Question

Divide the polynomials. The form of your answer should either be  p(x) or  p(x)+(k)/(x-3) where  p(x) is a polynomial and  k is an integer.  (x^(3)-4x-15)/(x-3)=◻

Bytelearn · Accepted Answer

Set up long division: Set up the long division. We will use polynomial long division to divide (x^3 - 4x - 15) by (x - 3).Divide first term of dividend by first term of divisor: Divide the first term of the dividend by the first term of the divisor. Divide x^3 by x to get x^2. Multiply (x - 3) by x^2 and subtract the result from the dividend. x^3 / x = x^2 (x - 3) * x^2 = x^3 - 3x^2Write down result and bring down next term: Write down the result and bring down the next term. After subtracting, we bring down the next term of the dividend, which is -4x. The new dividend is -3x^2 - 4x.Divide first term of new dividend by first term of divisor: Divide the first term of the new dividend by the first term of the divisor. Divide -3x^2 by x to get -3x. Multiply (x - 3) by -3x and subtract the result from the new dividend. -3x^2 / x = -3x (x - 3) * -3x = -3x^2 + 9xWrite down result and bring down next term: Write down the result and bring down the next term. After subtracting, we bring down the next term of the dividend, which is -15. The new dividend is 9x - 15.Divide first term of new dividend by first term of divisor: Divide the first term of the new dividend by the first term of the divisor. Divide 9x by x to get 9. Multiply (x - 3) by 9 and subtract the result from the new dividend. 9x / x = 9 (x - 3) * 9 = 9x - 27Write down result and find remainder: Write down the result and find the remainder. After subtracting, we find the remainder. The new dividend is -15 - (-27) = 12. The remainder is 12.Write final answer: Write the final answer. The quotient is x^2 - 3x + 9 with a remainder of 12. The final answer is in the form p(x) + (k)/(x - 3), where p(x) is the quotient polynomial and k is the remainder. p(x) = x^2 - 3x + 9 k = 12

Divide the polynomials. $\newline$ The form of your answer should either be $p(x)$ or $p(x)+\frac{k}{x-3}$ where $p(x)$ is a polynomial and $k$ is an integer. $\newline$ $\frac{x^{3}-4 x-15}{x-3}=\square$

Full solution

More problems from Powers with decimal and fractional bases

Related topics

Divide the polynomials.\newlineThe form of your answer should either be p(x) p(x) p(x) or p(x)+kx−3 p(x)+\frac{k}{x-3} p(x)+x−3k​ where p(x) p(x) p(x) is a polynomial and k k k is an integer.\newlinex3−4x−15x−3=□ \frac{x^{3}-4 x-15}{x-3}=\square x−3x3−4x−15​=□

Divide the polynomials. $\newline$ The form of your answer should either be $p(x)$ or $p(x)+\frac{k}{x-3}$ where $p(x)$ is a polynomial and $k$ is an integer. $\newline$ $\frac{x^{3}-4 x-15}{x-3}=\square$