Determine which of the following polynomials has (x + 1) a factor:x4 +

1.	Determine which of the following polynomials has (x + 1) a factor:x4 + 3x3 + 3x2 + x + 1
Answer» If (x + 1) is a factor of polynomial p(x) = x⁴ + 3x³ + 3x² + x + 1, then p(−1) must be 0, otherwise (x + 1) is not a factor of this polynomial. p(−1) = (−1)⁴ + 3(−1)³ + 3(−1)² + (−1) + 1 = 1 − 3 + 3 − 1 + 1 = 1 As p(−1) ≠ 0, Therefore, x + 1 is not a factor of this polynomial.

Determine which of the following polynomials has (x + 1) a factor:x4 + 3x3 + 3x2 + x + 1

Answer»

If (x + 1) is a factor of polynomial p(x) = x⁴ + 3x³ + 3x² + x + 1, then p(−1) must be 0, otherwise (x + 1) is not a factor of this polynomial.

p(−1) = (−1)⁴ + 3(−1)³ + 3(−1)² + (−1) + 1

= 1 − 3 + 3 − 1 + 1 = 1 As p(−1) ≠ 0,

Therefore, x + 1 is not a factor of this polynomial.