Question

What it means that [If x is a factor of p(x), what is the value of k?]

I can't understand [x is a factor of p(x)] and how i solve this question.

Answer 1

`k = -4`

Step-by-step explanation:

Given

`P(x) = (3x^2 - 5)(x + k) - 20`

x is a factor

Required

Solve for k

x is a factor means that the polynomial can be divided successfully by x.

In other words, x is a zero of the polynomial.

i.e.

`x = 0` and
`P(x) = 0`

Substitute 0 for x in P(x)

`P(x) = (3x^2 - 5)(x + k) - 20`

`P(x) = (3*0^2 - 5)(0 + k) - 20`

`P(x) = (0- 5)(k) - 20`

`P(x) = (-5)(k) - 20`

`P(x) = -5k - 20`

Substitute 0 for P(x)

`0 = -5k - 20`

Collect Like Terms

`5k = - 20`

Divide both sides by 5

`k = -4`