Question

Find the value of k if (x-1) is a factor of the polynomial x^3 +3x^2+5k+6

Answer 1

Answer:

here is your answer mate...

Step-by-step explanation:

x - 1 is a factor of 4x^3 + 3x^2 -4x +k

then x=1 is one root of 4x^3 + 3x^2 -4x +k

put x= 1

4x^3 +3x^2 -4x +k = 0

=> 4 (1)^3 +3 (1)^2-4 (1) +k =0

=> 4 + 3 - 4 + k = 0

=> k = -3

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Answer 2

Factor theorem: If (x-a) is a factor of p(x), then x=a is the zero/root of p(x).

Here:

(x-1) is a factor.

So, x=1 is the root of p(x)= x^3+3x^2+5k+6

Substitute the value of x obtained.

p(x) = x^3+3x^2+5k+6

p(x)= 1^3 + (3x1)^2+5k+6

p(x)=1+9+5k+6

p(x)=16+5k=0

p(x)=5k= -16

p(x)=k=-16/5

Hence, value of k= -16/5...