Q.2 Factorize the following by Factor theorem:
(a)x³ +9 x²+23x+15
(b) x³ -6 x² +11x-6
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a) x³ + 9x² + 23x +15
Factors of the constant term 15 = ± 1 , ± 3 , ± 5 , ± 15
- Let us pick any factor of constant randomly that when put at place of x gives 0
Let x = -1
x³ + 9x² + 23 x + 15
= (-1)³ + 9(-1)² + 23 (-1) + 15
= -1 + 9 -23 + 15
= 24 - 24
= 0
Let x = -3
(-3)³ + 9 (-3)² + 23 (-3) + 15
= -27 + 81 - 69 + 15
= 96 - 96
= 0
Let x = -5
(-5)³ + 9(-5)² + 23 (-5) + 15
= -125 + 225 - 115 + 15
= 240 - 240
x = -1 , -3 and -5
Therefore
x³ + 9x² + 23x +15 = (x+1)(x+3)(x+5)
_____________________________
b) x³ - 6x² +11x -6
Factors of constant 6 = ±1 , ±2 , ± 3 and ± 6
Let x = 1
(1)³ - 6(1)² + 11(1) - 6
= 1 -6 +11 -6
= 12-12
= 0
Let x = 2
(2)³ - 6(2)² + 11(2) - 6
= 8 - 24 + 22 - 6
= 30 - 30
= 0
Let x = 3
(3)³ - 6(3)² + 11(3) -6
= 27 - 54 + 33 - 6
= 60 -60
= 0
Hence , x = 1 , 2 and 3
Therefore ,
x³ - 6x² + 11x - 6 = (x-1)(x-2)(x-3)
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0
Answer:
a) x=-1,-3,-5 answer
b) x=1,2,3,answer
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