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Question
Question 13
x + 1 is a factor of the polynomial
A) x3+x2−x+1
B) x3+x2+x+1
C) x4+x3+x2+1
D) x4+3x3+3x2+x+1
x + 1 is a factor of the polynomial
A) x3+x2−x+1
B) x3+x2+x+1
C) x4+x3+x2+1
D) x4+3x3+3x2+x+1
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Solution
The answer is B.
Let assume (x+1) is a factor of x3+x2+x+1
So, x = -1 is zero of x3+x2+x+1
∴ (−1)3+(−1)2+(−1)+1=0
⇒ −1+1−1+1=0⇒0=0
Hence, our assumption is true.
Let assume (x+1) is a factor of x3+x2+x+1
So, x = -1 is zero of x3+x2+x+1
∴ (−1)3+(−1)2+(−1)+1=0
⇒ −1+1−1+1=0⇒0=0
Hence, our assumption is true.
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