Question

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

Answer 1

Answer:

$k = -4$

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

$k = -4$