SOLUTION: Two polynomials P and D are given. Use either synthetic or long division to divide P(x) by D(x), and express P in the form P(x) = D(x) · Q(x) + R(x). P(x) = 12x4 + 9x3 + 7x2,

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Two polynomials P and D are given. Use either synthetic or long division to divide P(x) by D(x), and express P in the form P(x) = D(x) · Q(x) + R(x). P(x) = 12x4 + 9x3 + 7x2,       Log On


   



Question 1007890: Two polynomials P and D are given. Use either synthetic or long division to divide
P(x) by D(x), and express P in the form P(x) = D(x) · Q(x) + R(x).
P(x) = 12x4 + 9x3 + 7x2, D(x) = 3x2 + 1

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
P%28x%29+=+12x%5E4+%2B+9x%5E3+%2B+7x%5E2
D%28x%29+=+3x%5E2+%2B+1+

P%28x%29+%2FD%28x%29=%2812x%5E4+%2B+9x%5E3+%2B+7x%5E2%29%2F%283x%5E2+%2B+1%29
---------(4x%5E2%2B3x%2B1=>Q%28x%29
%283x%5E2+%2B+1%29|12x%5E4+%2B+9x%5E3+%2B+7x%5E2
---------12x%5E4%2B0%2Ax%5E3%2B4x%5E2..........subtract
------------9x%5E3%2B3x%5E2%2B0%2Ax..........
------------9x%5E3%2B0%2Ax%5E2%2B3x...........subtract
---------------3x%5E2-3x.........
---------------3x%5E2%2B1...........subtract
-------------------3x-1..reminder R%28x%29
P%28x%29+=+D%28x%29+%2A+Q%28x%29+%2B+R%28x%29
12x%5E4+%2B+9x%5E3+%2B+7x%5E2=%283x%5E2+%2B+1%29%284x%5E2%2B3x%2B1%29+%2B%28-3x-1%29