Divide using polynomial long division

(x^2+x-17) / (x-4)

The solution for (x^2+x-17) / (x-4) is (x + 5) + 3 / (x-4)

Step-by-step explanation:

The given polynomial is (x^2+x-17) divided by (x-4)

Steps for long division method:

check the polynomial is written in descending order of power (x^3, x^2, and so on). To make the first term zero, multiply the divisor with one power lesser than the first term. For eg. To divide x^2, multiply the divisor with x. Subtract and bring down the next term. The above two steps are repeated until the last term gets divided. The term remaining after the last subtract step is the remainder. The final answer must be written in quotient and remainder as a fraction with the divisor.

Using long division method:

x + 5

x-4 | x^2 + x - 17

(-) (x^2 - 4x)

5x - 17

(-) (5x - 20)

3

The quotient is (x+5).

The remainder is 3.

The solution is written in the form of quotient + remainder / divisor

∴ The final answer is (x^2+x-17) / (x-4) = (x + 5) + 3 / (x-4)