If x²+x+1 is a factor of the polynomial 3x³+8x³+8x+3+5k what is the value of k
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Step-by-step explanation:
3x^3+8x^2+8x+3+5k
=3x(x^2+x+1)-3x^2–3x+8x^2+8x+3+5k
=3x(x^2+x+1)+5x^2+5x+3+5k
=3x(x^2+x+1)+5(x^2+x+1)-5+3+5k
=3x(x^2+x+1)+5(x^2+x+1)+5k-2
=(x^2+x+1)(3x+5)+5k-2
If we divide 3x^3+8x^2+8x+3+5k by x^2+x+1
the quotient = 3x+5 and remainder =5k-2 ,
But x^2+x+1 is a factor of given polynomial
therefore remainder should be zero.
5k - 2 = 0
5k =2
k = 2/5 , Answer
Answered by
2
Answer:
Step-by-step explanation:
3x^3+8x^2+8x+3+5k
=3x(x^2+x+1)-3x^2–3x+8x^2+8x+3+5k
=3x(x^2+x+1)+5x^2+5x+3+5k
=3x(x^2+x+1)+5(x^2+x+1)-5+3+5k
=3x(x^2+x+1)+5(x^2+x+1)+5k-2
=(x^2+x+1)(3x+5)+5k-2
If we divide 3x^3+8x^2+8x+3+5k by x^2+x+1
the quotient = 3x+5 and remainder =5k-2 ,
But x^2+x+1 is a factor of given polynomial
therefore remainder should be zero.
5k - 2 = 0
5k =2
k = 2/5 , Answer
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