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If (x+2)(x+5) is HCF of (x+2)(x2+6x+a) and (x+5)(x2+8x+b) find a and b

If (x+2)(x+5) is HCF of (x+2)(x2+6x+a) and (x+5)(x2+8x+b) find a and b

Grade:10

1 Answers

Vikas TU
14149 Points
6 years ago
HCF = (x+2)(x+5)
(x+2)(x+5) should be factor of (x+2)(x2+6x+a) hence by reminder theorem (x+5) can be factor of (x2+6x+a) only if x=-5.
=> (-5)2 + (6 x -5) + a = 0
=> 25 – 30 + a = 0
=> -5 + a = 0
=> a = 5.
 
(x+2)(x+5) should be factor of (x+5)(x2+8x+b) hence by reminder theorem (x+2) can be factor of (x2+8x+b) only if x=-2.
=> (-2)2 + (8 x -2) + b = 0
=> 4 – 16 + b = 0
=> -12 + b = 0
=> b = 12.

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