Plz help! I’ll mark brainliest!

Probably the easiest way to do this is to use synthetic division. We already know one of the zeros of the quadratic so we can use that number to find the other zero. If the point is (4, 0), then when y = 0, x = 4. Thus, 4 is a zero. Put 4 outside the "box" and put the coefficients from the quadratic inside, like this: 4 (1 -1 -12). Draw a line and bring down the first one under it. Multiply that 1 by the 4 to get 4. Put that 4 up under the -1 and add to get 3. Multiply 3 by 4 to get 12. Put that 12 up under the -12 and add to get 0. The numbers left under the line are the coefficients for the next polynomial, called the depressed polynomial, and this polyomial is one degree less than the one we started with. Those coefficients are 1 and 3. Therefore, the polynomial is x + 3 = 0. That means that the other zero, or x-intercept, is x = -3.

6 0

3 years ago

What is 2x3 - 5x2 - 4x - 25<br> divided by X - 4

Nonamiya [84]

Answer:

2x² + 3x + 8 + 7/x-4

Step-by-step explanation:

For this problem, we can use synthetic division.

4 | 2 -5 -4 -25

| 8 12 32

|_________

2 3 8 7/x-4

This means the quotient is 2x² + 3x + 8 + 7/x-4.

7 0

3 years ago

Write an equation for a rational function with: Vertical asymptotes at x = -4 and x = 2 x-intercepts at x = -2 and x = -3 Horizo

Dominik [7]

Answer:

Correct answer: y = ( 3x² + 15x + 18) / (x² + 2x - 8)

Step-by-step explanation:

The function has vertical asymptotes at points where it is not defined.

In our case it is at x₁ = -4 and x₂ = 2

This means that the function in the denominator has a quadratic function whose roots are (x + 4) · (x - 2) = x² + 2x - 8

The function intercepts x axis at x₀₁ = -2 and x₀₂ = -3

This means that the function in the numerator has a quadratic function whose roots are (x + 2) · (x + 3) = x² + 5x + 6

The function currently looks like this:

y = (x² + 5x + 6) / (x² + 2x - 8)

Since the function has a horizontal asymptote y = 3, this means when x strive to + - infinite or x -> + - ∞ then it is

lim x -> + - ∞ (x² + 5x + 6) / (x² + 2x - 8) = 3

This means that the function in the numerator must has term 3x² which we will get when we multiply the currently function y = (x² + 5x + 6) / (x² + 2x - 8) by the number 3 and get :

y = 3 · (x² + 5x + 6) / (x² + 2x - 8) = (3x² + 15x + 18) / (x² + 2x - 8)

y = ( 3x² + 15x + 18) / (x² + 2x - 8)

God is with you!!!

4 0

2 years ago