Use the factor theorem to determine whether g(x) is a factor of p(x) in each of the following cases:.
(i) p(x)=2x³+x²-2x-1,g(x)=x+1.
(ii)p(x)=x³+3x²+3x+1,g(x)=x+2.
(iii)p(x)=x³-4x²+x+6,g(x)=x-3.
Answers
Answer: ur ans
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
Answer:1. here is the answer
If g(x)=x+1 is a factor of the given polynomial p(x),then p(-1)must be zero
P(x)=2x²+x²-2x-1
P(-1)=2(-1)³+(-1)²-2(-1)-1
=2(-1)+2+2-1=0
Hence,g(x)=x+1is factor of the given polynomial
Hope it helps you ☺️ ☺️
Step-by-step explanation: