Math, asked by sunilbhuya359, 4 hours ago

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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Answers

Answered by rahulswag
0

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 Anonymous
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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