Question

determine which of the following polynomials has (x+1) a factor
(1). x³-x²-(2+✓2)x+✓2​

Answer 1

Step-by-step explanation:

factor=(x+1)

so x+1=0

=>x=-1

(i) p(x)=x³+x²+x+1

p(-1)=(-1)³+(-1)²+(-1)+1

=-1+1-1+1

=0

so (x+1) is the factor of x³+x²+x+1

(ii) p(x)= x^4+x³+x²+x+1

p(-1)=(-1)^4+(-1)³+(-1)²+(-1)+1

=1-1+1-1+1

=1

so (x+1) is not the factor of x^4+x³+x²+x+1

(iii) p(x)=x^4+3x³+3x²+x+1

p(-1)=(-1)^4+3(-1)³+3(-1)²+(-1)+1

= 1-3+3-1+1

= 1

so (x+1) is not the factor of x^4+3x³+3x²+x+1

(iv) p(x)=x³-x²-(2+√2)x+√2

[ note i have changed 2^(1/2) to √2 because they are equal ]

p(-1)=(-1)³-(-1)²-(2+√2)(-1)+√2

= -1-1-(-2-√2)+√2

= -2+2+√2+√2

= 2√2

so x³-x²-(2+√2)x+√2 don't have (x+1) as a factor.

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