Can someone explain to me?

Question

f(x) - f(p)/x - p
To: f(x) = x² - 3x , p = -2

Thanks!!!

Answer 1

Given: f(x) - f(p)/x - p
And: f(x) = x² - 3x
And: p = -2

Fit the given information f(x) - f(p)/x into the formula:
f(x) - f(p)/x - p = (x² - 3x) - (-2/ x - (-2))
f(x) - f(p)/x - p = (x² - 3x) - (-2/ x + 2)
f(x) - f(p)/x - p = x² - 3x + 2/ x + 2)
f(x) - f(p)/x - p = x² - 3x + 2x^-1 + 2

Answer 2

Sudha made a slight error;
He was right up to x^2 - 3x -10/x + 2
I'd just leave it there, but if you want to factorize the quadratic you're looking at x^2 - 3x + 2, (x+3)(x-1).

You wanted an explanation; when you express something as f(x) that means that you plug x into the equation and see what falls out. f(x) Usually can't be evaluated, because x is not constant/is not known, so f(x) is used to describe the function. p Is known, so we can evalutate the function, essentially at the point x=p. As p=-2, you could express it as f(-2)=10.

Answer 3

f(p) = 4 - 3*(-2) = 4 + 6 = 10 (put the value of p instead of x in f(x))

So the entire funtion becomes
x^2 - 3x - 10 / x - (-2) = x^2 - 3x - 10 / x + 2

On factorizing x^2 - 3x - 10 => (x+2)(x-5)

So net answer would be x-5.

Answer 4

Do what?