SOLUTION: Find the quotient and remainder when p(x) is divided by q(x), where p(x) = 9x^4 + x^3 - 12x + 21 and q(x) = x.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find the quotient and remainder when p(x) is divided by q(x), where p(x) = 9x^4 + x^3 - 12x + 21 and q(x) = x.      Log On


   

Question 1209674: Find the quotient and remainder when p(x) is divided by q(x), where p(x) = 9x^4 + x^3 - 12x + 21 and q(x) = x.
Answer by CPhill(1987) About Me  (Show Source):
You can put this solution on YOUR website!
When dividing a polynomial by a monomial (like 'x' in this case), the process is straightforward: simply divide each term of the polynomial by the monomial.
* p(x) = 9x⁴ + x³ - 12x + 21
* q(x) = x
Dividing each term of p(x) by q(x):
* (9x⁴)/x = 9x³
* (x³)/x = x²
* (-12x)/x = -12
* 21/x = 21/x
Therefore:
* **Quotient:** 9x³ + x² - 12
* **Remainder:** 21