Question

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

Answer 1

Answer: I got this answer wrong but I go two right look at the step by step explanation

Hopefully that helped a little

Step-by-step explanation:

Answer 2

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,

$f(x) = x^3+3x^2-25x-75$

Equate (x + 5) is equal to 0.

x + 5 = 0

x = -5

Substitute x = -5 in given equation.

$f(x) = x^3+3x^2-25x-75\\\\f(-5) = -5^3+3(-5)^2-25(-5)-75\\\\f(-5) = 0$

         

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

Learn more about the remainder theorem here:

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