Question

CAN SOMEONE HELP PLZZZZ ALGEBRA

Answer 1

Answer: K = 196

Step-by-step explanation:

We are given the equation
`f(x) = x^(3) -4x+k`, and we are also given the fact the the 91 is left when the value of x = -5. We have to find the value of k.

1. The first step is to substitute the x for -5.

2. After substituting the x for -5 in all places, ad =91 to make it an equation because we know that 91 will remain. After that, simplify the equation.

-4(-5) becomes 20 because multiplying a negative factor by itself or another negative factor makes the product a positive.

3. Once finished simplifying, add 105 to both sides of the equation in order to get the variable by itself.

1.
`f(x) = x^(3) -4x+k`

`-5^(3) -4(-5)+k`

2.
`-5x^(3) -4(-5)+k = 91`

`-125+20+k=91`

`-105+k=91`

3. -105 + k = 91

+105 +105

`k = 196`

Hope this helps!

Answer 2

Explanation:

The remainder theorem says that when you put the integer part of the binomial for the value of x in f(x), you can solve for the remainder.

f(x) = x^3 - 4x + k is divided by (x - 5) means that 5 is put into f(x)

f(5) = x^3 - 4x + k now put 5 into x on the right

f(5) = 5^3 - 4(5) + k

f(5) = 125 - 20 + k = 91

f(5) = 105 + k = 91

105 + k = 91 Subtract 105 from both sides

k = 91 - 105

k = -14