Divide the polynomials. Your answer should be in the form p(x)+(k)/(x+3) where p is a polynomial and k is an integer. (x^(2)-7)/(x+3)=

Question

Divide the polynomials. Your answer should be in the form  p(x)+(k)/(x+3) where  p is a polynomial and  k is an integer.  (x^(2)-7)/(x+3)=

Bytelearn · Accepted Answer

Set up division: Set up the division of the polynomials using long division. We are dividing (x^2 - 7) by (x + 3). We will use polynomial long division to find the quotient and remainder.Determine divisor count: Determine how many times the divisor (x + 3) goes into the first term of the dividend (x^2). The first term of the divisor is x, and it goes into the first term of the dividend, x^2, exactly x times because x * x = x^2.Multiply and subtract: Multiply the divisor (x + 3) by the result from Step 2 (x) and subtract it from the dividend (x^2 - 7). (x + 3) * x = x^2 + 3x Now subtract this from the dividend: (x^2 - 7) - (x^2 + 3x) = -3x - 7Bring down and repeat: Bring down the next term of the dividend, if any, and repeat the process. Since there are no more terms to bring down, we proceed to the next step.Determine new divisor count: Determine how many times the divisor (x + 3) goes into the new term from Step 3 (-3x - 7). The divisor goes into -3x, -3 times because -3 * x = -3x.Multiply and subtract again: Multiply the divisor (x + 3) by the result from Step 5 (-3) and subtract it from the new term (-3x - 7). (x + 3) * -3 = -3x - 9 Now subtract this from the new term: (-3x - 7) - (-3x - 9) = -3x - 7 + 3x + 9 = 2Write final answer: Write the final answer in the form p(x) + (k)/(x + 3), where p(x) is the quotient and k is the remainder. The quotient from our division is x - 3, and the remainder is 2. Therefore, the final answer is: p(x) = x - 3 k = 2

Divide the polynomials. Your answer should be in the form $p(x)+\frac{k}{x+3}$ where $p$ is a polynomial and $k$ is an integer. $\newline$ $\frac{x^{2}-7}{x+3}=$

Full solution

More problems from Negative Exponents

Related topics

Divide the polynomials. Your answer should be in the form p(x)+kx+3 p(x)+\frac{k}{x+3} p(x)+x+3k​ where p p p is a polynomial and k k k is an integer.\newlinex2−7x+3= \frac{x^{2}-7}{x+3}= x+3x2−7​=

Divide the polynomials. Your answer should be in the form $p(x)+\frac{k}{x+3}$ where $p$ is a polynomial and $k$ is an integer. $\newline$ $\frac{x^{2}-7}{x+3}=$