Answer:
- x² - 8x + 12
- x³ + 2x² - 15x - 36
- x³ -2x² - 15x
Explanation:
#1) Find the polynomial with roots at 2 and 6
- (x -2)(x - 6) = x² - 8x + 12
#2) Find the polynomial with a double root at -3 and another root at 4
- (x+3)(x+3)(x-4) = (x²+6x+9)(x-4) = x³ + 2x² - 15x - 36
#3) Find the polynomial with roots 0, -3 and 5
- (x -0)(x+3)(x-5) = x(x²-2x - 15) = x³ -2x² - 15x