SAT College

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.

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

Answers

Answer 1

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]

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Answers

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Answers

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