SOLUTION: If (x-2) is one factor of the polynomials x²+ax-6 and x²-9x+b, then a+b is equal to........
a) 15
b) 13
c) 11
d) 10
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-> SOLUTION: If (x-2) is one factor of the polynomials x²+ax-6 and x²-9x+b, then a+b is equal to........
a) 15
b) 13
c) 11
d) 10
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Question 823795: If (x-2) is one factor of the polynomials x²+ax-6 and x²-9x+b, then a+b is equal to........
a) 15
b) 13
c) 11
d) 10 Answer by TimothyLamb(4379) (Show Source):
You can put this solution on YOUR website! ---
(x - 2) is common factor
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x^2 + ax - 6 = (x - 2)(x + K)
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(x - 2)(x + K)
x^2 + Kx - 2x - 2K
x^2 + (K - 2)x - 2K
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-2K = -6
K = 3
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K - 2 = a
3 - 2 = a
a = 1
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x^2 + x - 6 = (x - 2)(x + 3)
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second factor of x^2 + ax - 6 is (x + 3)
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x^2 - 9x + b = (x - 2)(x + K)
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(x - 2)(x + K)
x^2 + Kx - 2x - 2K
x^2 + (K - 2)x - 2K
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K - 2 = -9
K = -7
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-2K = b
b = -2(-7)
b = 14
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x^2 - 9x + 14 = (x - 2)(x - 7)
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second factor of x^2 - 9x + b is (x - 7)
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answer:
a + b = 15
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