X3 +25x 2 +50x−1000 spacex, start superscript, 3, end superscript, plus, 25, x, start superscript, 2, end superscript, plus, 50, x, minus, 1000 the polynomial above has (x-5)(x−5)left parenthesis, x, minus, 5, right parenthesis and (x+10)(x+10)left parenthesis, x, plus, 10, right parenthesis as factors. what is the remaining factor?

p(x) = x³+25x²+50x-1000 = (x-5)(x+10)(x+20)

Step-by-step explanation:

p(x) = x³+25x²+50x-1000

p(x) = (x-5)(x+10)(x-a)

x-a = ?

We can use Briot-Ruffini to find out.

As x-5 is a factor, we know that x-5=0 gives a root, so x=5 is a root of p(x)

As x+10 is a factor, we know that x+10=0 gives a root, so x=-10 is a root of p(x)

5   | 1   25    50    -1000

10 | 1   30    200   |   0

    | 1   20   |   0

x + 20

So, p(x) = (x-5)(x+10)(x+20)