10. Determine whether x - 1 is the factor of x2 - 2x + 1 or not?
Answers
Step-by-step explanation:
Explanation:
Answer:
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Solution: (i) p(x) = 2x3 + x2 � 2x � 1, g(x) = x + 1
Apply remainder theorem
=>x + 1 =0
=> x = - 1
Replace x by � 1 we get
=>2x3 + x2 � 2x � 1
=>2(-1)3 + (-1)2 -2(-1) - 1
=> -2 + 1 + 2 �- 1
=> 0
Remainder is 0 so that x+1 is a factor of 2x3 + x2 � 2x � 1
(ii) p(x) = x3 + 3x2 + 3x + 1, g(x) = x + 2
Apply remainder theorem
=>x + 2 =0
=> x = - 2
Replace x by � 2 we get
=>x3 + 3x2 + 3x + 1
=>(-2)3 + 3(-2)2 + 3(-2) + 1
=> -8 + 12 - 6 + 1
=> -1
Remainder is not equal to 0 so that x+2 is not a factor of x3 + 3x2 + 3x + 1
(iii) p(x) = x3 � 4x2 + x + 6, g(x) = x � 3
Apply remainder theorem
=>x - 3 =0
=> x = 3
Replace x by � 2 we get
=>x3 � 4x2 + x + 6
=>(3)3 -4(3)2 + 3 + 6
=> 27� - 36�� +3 + 6
=> 0
Solution: (i) p(x) = 2x3 + x2 � 2x � 1, g(x) = x + 1
Apply remainder theorem
=>x + 1 =0
=> x = - 1
Replace x by � 1 we get
=>2x3 + x2 � 2x � 1
=>2(-1)3 + (-1)2 -2(-1) - 1
=> -2 + 1 + 2 �- 1
=> 0
Remainder is 0 so that x+1 is a factor of 2x3 + x2 � 2x � 1
(ii) p(x) = x3 + 3x2 + 3x + 1, g(x) = x + 2
Apply remainder theorem
=>x + 2 =0
=> x = - 2
Replace x by � 2 we get
=>x3 + 3x2 + 3x + 1
=>(-2)3 + 3(-2)2 + 3(-2) + 1
=> -8 + 12 - 6 + 1
=> -1
Remainder is not equal to 0 so that x+2 is not a factor of x3 + 3x2 + 3x + 1
(iii) p(x) = x3 � 4x2 + x + 6, g(x) = x � 3
Apply remainder theorem
=>x - 3 =0
=> x = 3
Replace x by � 2 we get
=>x3 � 4x2 + x + 6
=>(3)3 -4(3)2 + 3 + 6
=> 27� - 36�� +3 + 6
=> 0