Question

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Use the Remainder Theorem to determine which binomial is a factor of the function f(x) = x^3 − 19x + 30.

A. (x + 2)
B. (x + 3)
C. (x + 5)
D. (x − 5)

Answer 1

Hey There!

In order to solve this you need to factor f(x) = x^3 - 19x + 30 Entirely.

When you do that you get these factors;

f(x) = (x – 2) (x – 3) (x + 5)

From there you play 'elimination'

A) There is no listed factor for (x + 2)

B) There is no listed factor for (x + 3)

C) There is a listed factor for (x + 5)!

D) There is no listed factor for (x - 5)

Hope I helped, Five Stars & Brainliest always helps!

Answer 2

The binomial (x+5) is the  factor of the function $f(x) = x^3 - 19x + 30$

What is factorization?

Factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.

Now we will put the value of the x in the function if the value of the function is zero then that will be the factor.

$f(x)=x^3-19x+30$

$f(-2)=(-2^3)-19(-2)+30=60 \ \ \ \ not \ Zero$

$f(-3)=(-3^3)-19(-3)+30=50\ \ \ \ \ not \ \ Zero$

$f(-5)=(-5^3)-19(-5)+30=-125+125=0 \ \ \ Equal\ \ to \ Zero$

So at x=-5 the value of the function is zero. Hence (x+5) will be the factor of the given function.

To know more about factorization follow

https://brainly.com/question/25829061

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