If ( x-2 ) and (x +3) are factors of x3 + ax2 +bx -30, find a and b.
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f(x) = x-2
x = 2
p(2) = 2³ + 4a + 2b - 30
= 8 + 4a + 2b - 30
= 4a + 2b - 28.
p(-3) = -27 + 9a - 3b - 30
= 9a - 3b - 57
4a + 2b - 28 = 9a - 3b - 57
2b - 28 = 5a - 3b - 57
5b - 28 = 5a - 57
5(a-b) = -29
a-b = -5.8
x = 2
p(2) = 2³ + 4a + 2b - 30
= 8 + 4a + 2b - 30
= 4a + 2b - 28.
p(-3) = -27 + 9a - 3b - 30
= 9a - 3b - 57
4a + 2b - 28 = 9a - 3b - 57
2b - 28 = 5a - 3b - 57
5b - 28 = 5a - 57
5(a-b) = -29
a-b = -5.8
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