SOLUTION: (x4 − x2 + 3x − 10) ÷ (x + 5) divide the polynomials by either long division or synthetic division.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: (x4 − x2 + 3x − 10) ÷ (x + 5) divide the polynomials by either long division or synthetic division.      Log On


   

Question 812929: (x4 − x2 + 3x − 10) ÷ (x + 5)
divide the polynomials by either long division or synthetic division.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Whether you use long or synthetic division, it is important to notice that there is no x%5E3 term in the dividend!

%28x%5E4+-x%5E2+%2B+3x+-+10%29+%2F+%28x+%2B+5%29
Since synthetic division is usually easier I choose to divide this way. Since synthetic division is designed to work with divisors in the form of (x - c) [where 'c' is some number], we must think of the x+5 as x-(-5):
-5 |    1   0   -1     3   -10
----       -5   25  -120   585
       ------------------------
        1  -5   24  -117   575

The number in the lower right, 575, is the remainder. The rest of the bottom line is the quotient. The quotient of "1 -5 24 -117" translates into: x%5E3-5x%5E2%2B24x-117. So, after putting the remainder over the divisor, we get: