Question

If x2+x+1 is a factor of the polynomial 3x3+8x2+8x+3+5k,then the value of k

Answer 1

3 ×3 + 8 × 2+8×(-1/2)+3+5K=0

9 + 16 -4 +3 + 5K= 0

28 - 4 +5K = 0

24 + 5K = 0

5K = (-24)

K = (-24/5)

Answer 2

Answer:

$k=\frac{2}{5}$

Step-by-step explanation:

Given: $x^{2} +x+1$  is a factor of the polynomial $3x^{3}+8x^{2} +8x+3+5k$.

To find value of k.

Using division algorithm i.e; dividend=divisor* quotient + remainder

we have;

$3x^{3}+8x^{2} +8x+3+5k=(x^{2} +x+1)(3x+5)+(-2+5k)$

But since it is given that $x^{2} +x+1$ is factor of $3x^{3}+8x^{2} +8x+3+5k$ it means that remainder must be 0.

So, we have

$-2+5k=0\\5k=2\\k=\frac{2}{5}$

Hence value of k is $\frac{2}{5}$.

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