Question

Determine which of the following polynomials has (x + 1) a factor :
(i) x + x2 + x + 1
(ii) x + x3 + x2 + x + 1
(iii) x + 3x + 3x2 + x + 1
(iv) x - x - (2 + 12)x+ 12
please help it,s urgently ​

Answer 1

Step-by-step explanation:

x +1 =0

x =0 - 1

x = - 1

p(x) = x + x² + x + 1

p(-1) = - 1 +(-1) +(-1) +1

= - 1 - 1 - 1 +1

= - 2 - 1 +1

= - 3 +1

= - 2

It is not a factor

p(x) = x + x³ + x² + x + 1

p(-1) = - 1 +(-1)³+(-1)² +(-1)+1

= - 1 - 1 + 1 - 1 + 1

= - 2 + 1

= - 1

It is not a factor

p(x) = x + 3x + 3x² + x + 1

p(-1) = - 1 +3(-1) +3(-1)² +(-1) +1

= - 1 - 3 + 3 - 1 +1

= - 1

It is not a factor

p(x) = x - x - (2+12)x +12

p(-1) = - 1 - (-1) - (2+12)-1 +12

= - 1 - 1 - 2 + 12 - 1 +12

= - 2 - 2 + 12 - 1 +12

= - 4 +12 - 1 +12

= 8 - 1 +12

= 7 +12

= 19

It is not a factor