Question

1-x-x²-3x³,2x²+x³+3,x²+5x-2,x³-x²-3x​

Answer 1

Step-by-step explanation:

Let x + 1 is a factor of given polynomial.

Now, x + 1 = 0

x = -1

p(-1) = (-1)³ + (-1)² + (-1) + 1

= -1 + 1 - 1 + 1

= 2 - 2 = 0

Therefore, It is confirmed that x + 1 is a factor of x³ + x² + x + 1.

(ii) x⁴ + x³ + x² + x + 1

Let x + 1 is a factor of given polynomial.

Now, x + 1 = 0

x = -1

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

= 1 - 1 + 1 - 1 + 1

= 3 - 2 = 1

Therefore, x + 1 is not a factor of x⁴ + x³ + x² + x + 1.

(iii) x⁴ + 3x³ + 3x² + x + 1

Let x + 1 is a factor of given polynomial.

Now, x + 1 = 0

x = -1

p(-1) = (-1)⁴ + 3 x (-1)³ + 3 x (-1)² + (-1) + 1

= 1 - 3 + 3 - 1 + 1

= 5 - 4 = 1

Therefore, x + 1 is not a factor of x⁴ + 3x³ + 3x² + x + 1.