Algebra 2?

1) (-3 + x) (-2 + x) (7 + x)

2) P(1) = 0

long divide the equation by x+7 so you sendup with the quadratic x^2 - 5x + 6 then factorises that to get (x + 3)(x + 2). sub 1 in to x^5 + 3x^4 + 3x - 7 and you get 0 therefor factor and you can long divide that by x-1 to get x^4 + 4x^3 + 4x^2 + 4x + 7 and just keep on until you get all 5 factors.

1....2....-29.....42...|..-7

.....-7.....35....-42

1....-5......6.....0

x² - 5x + 6

I don't understand the second part. If you want to find P(1), why would you use synthetic division and the remainder theorem? P(1) = 1^5 + 3×1^4 + 3×1 - 7 = 1 + 3 + 3 - 7 = 0

The answer is either -8,-6,0 or 1 for the second one.