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Answer:
[tex]k = -4[/tex]
Explanation:
Given
[tex]P(x) = (3x^2 - 5)(x + k) - 20[/tex]
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.
[tex]x = 0[/tex] and [tex]P(x) = 0[/tex]
Substitute 0 for x in P(x)
[tex]P(x) = (3x^2 - 5)(x + k) - 20[/tex]
[tex]P(x) = (3*0^2 - 5)(0 + k) - 20[/tex]
[tex]P(x) = (0- 5)(k) - 20[/tex]
[tex]P(x) = (-5)(k) - 20[/tex]
[tex]P(x) = -5k - 20[/tex]
Substitute 0 for P(x)
[tex]0 = -5k - 20[/tex]
Collect Like Terms
[tex]5k = - 20[/tex]
Divide both sides by 5
[tex]k = -4[/tex]