Question

find the value of k, if x-1 is a factor of 5xcube + 4x square -8x+k​

Answer 1

Answer:

PLEASE REFER THE ATTACHMENT FOR THE SOLUTION.

Answer 2

Solution:

➡ It is given that (x-1) is a factor of 5x³ + 4x² - 8x + k.

➡ We need to find the value of constant, k.

Applying the factor theorem here, 1 is a factor of g(x) which means that it will be a factor of p(x) as well.

This means that:

$\sf{\implies\:p(1)=g(1)=0}$

As it is given that (x-1) is a factor of the expression, we can write it as:

$\sf{\longrightarrow\:p(x)=5x^3+4x^2-8x+k}$

$\sf{\maltese\:g(x)=x-1}$

Henceforth:

$\sf{\longrightarrow\:g(1)=5\times(1)^3+4\times(1)^2-8\times1+k}$

$\sf{\longrightarrow\:g(1)=5+4-8+k}$

$\sf{\longrightarrow\:g(1)=9-8+k}$

$\sf{\longrightarrow\:g(1)=1+k}$

We know that if p(x) is a factor of an expression, then p(x) is equal to 0.

So,

$\sf{\longrightarrow\:1+k=0}$

$\sf{\longrightarrow\:k=0-1}$

$\sf{\longrightarrow\:k=-1}$

Hence the value of the constant "k" is -1.

Note:

If g(x) is a factor of an expression, then it means that the value of p(x) is 0. Also a factor x - constant refers that that g(x) is positive and a factor x + constant refers that g(x) is negative.

For example:

✳ If x - 2 is a factor, then g(x) = g(2).

✳ If x + 5 is a factor, then g(x) = g(-5).