Question

use the Factor. Theorem to determine whether g(x) is a factor of p(x)
p(x)=x³+3x²+3x+1 and g(x)=x+1 ​

Answer 1

Step-by-step explanation:(ii) p(x) = x3 + 3x2 + 3x + 1, g(x) = x + 2Apply remainder theorem=>x + 2 =0=> x = - 2Replace x by – 2 we get=>x3 + 3x2 + 3x + 1=>(-2)3 + 3(-2)2 + 3(-2) + 1=> -8 + 12 - 6 + 1=> -1Remainder is not equal to 0 so that x+2 is not a factor of x3 + 3x2 + 3x + 1

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Answer 2

Answer:

yes ..

Step-by-step explanation:

Given polynomial p(x) =x^3+3x^2+3x+1 is the factor of g(x)=x+1

If x+1 is factor then x+1=0 or x=-1

Replace x in p(x) by -1 we get

p(x)= x^3+3x^2+3x+1

after replacement ...

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

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

p(-1)=0

so p(x) is zero by g(x) = x+1 then g(x)=x+1 is factor of p(x) =x^3+3x^2+3x+1

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