Question

the value of k,if(x-1) 9s a factor of 4x^3+3x^2-4x+k,is​

Answer 1

Answer:

The value of k = (-3)

Step-by-step explanation:

To find the value of k, if (x - 1) is a factor of 4x^3 + 3x^2 -4x + k

Step 1 = Follow factor theorem

According to the factor theorem if (x - 1) is a factor of 4x^3 + 3x^2 - 4x + k then after substituting x = 1(x - 1 = 0 =  x = 1) that is zero of x - 1 in the polynomial 4x^3 + 3x^2 - 4x + k the value comes zero p(x) = 0

                                                                       p(1) = 0

So,

p(x) = 4x^3 + 3x^2 - 4x + k

p(1)[x = 1] = 4(1)^3 + 3(1)^2 - 4(1) + k

               = 4 + 3 - 4 + k

               = 4 - 4 + 3 + k

               = 3 + k

As we know that x -1 is a factor of the p(x) so p(1)[x = 1] = 0

Now,

= 3 + k

3 + k = 0

k = (-3)

Answer 2

- 3

Step-by-step explanation:

Given:

(x - 1) is the factor of above mentioned equation.

To find:

The value of k

Solution:

We have to do nothing just substitute the value in equation and answer will be yours.

Since, x - 1 is a factor.

Therefore, x - 1 = 0 ⟹ x = 1

Now, Putting the value of x in equation,

$4 {x}^{3} + 3 {x}^{2} - 4x + k \\ \\ 4 {( 1)}^{3} + 3 {(1)}^{2} - 4(1) + k = 0 \\ \\ 4 + 3 - 4 + k = 0 \\ \\ 3 + k = 0 \\ \\ k = - 3$

Therefore, The value of k is - 3.

Extra Information

Polynomial: A consist of constant, coefficient and variable with natural power is known as polynomial.

i.e x² + 5x + 2 is a polynomial.

x² is a veriable with natural power 2.

5x 5 is a coefficient with variable x.

2 is constant.