please give me this question answers who give me correct answer I will mark brainliest answer
Answers
Answer:
Step-by-step explanation:
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
Remainder is equal to 0 so that x-3 is a factor of x3 – 4x2 + x + 6
3Roman
Solution: (i) p(x) = x2 + x + k
Apply remainder theorem
=>x - 1 =0
=> x = 1
According to remainder theorem p(1) = 0 we get
Plug x = 1 we get
=> k(1)2 + 1+ 1 =0
=>k +1 + 1 =0
=> k + 2 = 0
=> k = - 2
Answer value of k = -2
(ii) p(x) = 2x2 + kx + √2
Apply remainder theorem
=>x - 1 =0
=> x = 1
According to remainder theorem p(1) = 0 we get
Plug x = 1 we get
p(1) = 2(1)2 + k(1) + √2
p(1) =2 + k + √2
0 = 2 + √2 + k
-2 - √2 = k
- (2 + √2) = k
Answer is k = - (2 + √2)
(iii) p(x) = kx2 – √2x + 1
Apply remainder theorem
=>x - 1 =0
=> x = 1
According to remainder theorem p(1) = 0 we get
Plug x = 1 we get
p(1) = k(1)2 – √2(1)+ 1
P(1) = K - √2 + 1
0 = K - √2 + 1
√2 -1 = K
Answer k= √2 -1
(iv) p(x) = kx2 – 3x + k
Apply remainder theorem
=>x - 1 =0
=> x = 1
According to remainder theorem p(1) = 0 we get
Plug x = 1 we get
P(1) = k(1)2 -3(1) + k
0= k – 3 + k
0 = 2k – 3
3 = 2k
3/2 = k
Answer k = 3/2