Question

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

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Let $p(x) = x^3+x^2+x+1$

The zero of x+1 is -1. [x+1 = 0 means x = -1]

$p(−1) = (−1)^3+(−1)^2+(−1)+1$

= −1+1−1+1

= 0

∴By factor theorem, x+1 is a factor of $x^3+x^2+x+1$

Answer 2

SOLUTION:-

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factor-(x+1)

so xt1-0

=>X=-1

(i) px)=x*+x+x+1

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

=-1t1-1t1=0

so (x+1) is the factor of x+x*+x+1

(i) Pt= x4+x+x+x+1

p(-1-1)4+(-1) (-12+(-1)+1

=1-1+1-1+1

so (x+1) is not the factor of x4+xx+x+1

(ii) p(x)=xA4+3x+3x2+x+1

PE1F-14+3(-1)*+34-1)+E1+1

1-3+3-1+1=1

so (x+1) is not the factor of x4+3x+3x?+x+1

(v) pix}=x-x-(2+/2)xtv2

[ note i have changed 2 (1/2) to v2 because

they are equal]

p(-1--11P-41)?-(2+V2}-1)+/2

-1-1-(-2-v2)+V2

-2+2t2+V222

so x'-x-(2+V2)x+/2 don't have (x*1) as a factor.