Question

Find k so that (x-2) is a factor of x³+kx-4

Answer 1

Answer:

as x-2 is factor

so x= 2

put in x^3+kx-4=0

2^3+2k-4=0

8+2k-4=0

2k =-4

k =-2

Answer 2

The value of k is -2.

Step-by-step explanation:

Given:

• A polynomial ${x}^{3} + kx - 4$.
• A factor of polynomial is $(x - 2)$.

To find:

• Find the value of k.

Solution:

Concept/Theorem to be used:

Factor theorem: If $(x - a)$ is a factor of polynomial p(x), then $\bf p(a) = 0$

Step 1:

Find the value of x form the given factor.

$x - 2 = 0$

or

$\bf x = 2$

Step 2:

Put x=2 in the polynomial.

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

or

$8 + 2k - 4 = 0$

or

$2k = - 4$

or

$\bf \red{k = - 2}$

Thus,

The value of k is -2, if (x-2) is a factor of polynomial $\bf {x}^{3} + kx - 4$.

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