x 3 + 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?

Answer: 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)