Question

Find the equation of a real cubic polynomial which cuts the X -axis at 2,the y-axis at -4 and passes through (1,-1) and (-1,-21)

Answer 1

You have 4 points to use with y = ax^3+bx^2+cx+d
8a+4b+2c+d = 0
d = -4
a+b+c+d = -1
-a+b-c+d = -21
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4a+2b+c = 2
a+b+c = 3
-a+b-c = -17
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3a+b = -1
2b = -14, so b = -7, a = 2, c=8

y = 2x^3 - 7x^2 + 8x - 4 = (x-2)(2x^2-3x+2)