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Use the remainder theorem to verify this statement.
(x+5) is a factor of the function f(x) = x^3 + 3x^2 - 25x - 75
1. Find the (product, quotient, difference, sum) of f(x) and x + 5
2. The (quotient, remainder, sum, discriminant) of this operation is 0
3. Therefore, (x+5) is (not a factor, the opposite, a factor, the simplified form) of function f
4. So f ([-75, 5, -5, 75)] = 0

Respuesta :

bennett40922

1. quotient

2.remainder

3. a factor

4. 5

Step-by-step explanation:

i just took the test

The expression (x + 5) is a factor of given function f(x).

So the remainder of the function will be zero.

Remainder theorem:

The given function is,

                      [tex]f(x) = x^3 + 3x^2 - 25x - 75[/tex]

We have to check (x + 5) is a factor of the given function.

Equate (x + 5) is equal to 0.

           x + 5 = 0

                 x = -5

Substitute x = -5 in given equation.

          [tex]f(-5)=(-5)^3+3(-5)^2-25(-5)-75\\\\f(-5)=-125+75+125-75\\\\f(-5)=0[/tex]

Since f(-5) = 0. Therefore, (x + 5) is a factor of given function f(x).

Learn more about the remainder theorem here:

https://brainly.com/question/13328536

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