Question

Determine which of the following polynomials has
(x + 1)a factor :
(iii) x^4+ 3x^3+ 3x^2+ x + 1​​

Answer 1

Step-by-step explanation:

Let p(x)= x⁴+3x³+3x²+x+1

Given, (x + 1) is a factor of p(x).

The zero of x+1 is x + 1 = 0 => x = -1.

On putting x= -1

p(−1)=(−1)⁴+3(−1)³+3(−1)²+(−1)+1

=> 1 − 3  + 3 − 1 + 1

=> 1 ≠ 0

Hence,by factor theorem,

x+1 is not a factor of x⁴+3x³+3x²+x+1

Hope it helps!

Answer 2

Answer:

Given:

• Determine which of the following polynomials has (x + 1)a factor : (iii) x^4+ 3x^3+ 3x^2+ x + 1.

Find:

• Find whether the polynomial is a factor or not.

Calculations:

• Let x be the common variable to this question.
• We know that the given equation is, x⁴+3x³+3x²+x+1 and the given value is (x + 1) is a factor of 'x)

= Zero = (x + 1)

= (x + 1) = 0

= (x = - 1)- Equation (1)

Adding the value from equation (1) [x= -1], we get:

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

= 1 - 3 + 3 - 1 + 1

= 1 ≠ 0

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