Question

Help with question 7!

Answer 1

a.
`x^2(x+4)(x-3)`

b.
`(x+6)(x+2)^2(x-1)`

Explanation:

a. The equation of a polynomial can be written using its graph by finding the x-intercepts.

The graph has x-intercepts -4, 0, and 3. The x-intercepts are the solutions from the factors of the equation. -4 resulted from x+4. 0 resulted from x except at 0 it doesn't cross through. It touches meaning it has an even exponent likely
`x^2`. And 3 resulted from x-3. Putting these factors together is the equation in factored form.

`x^2(x+4)(x-3)`

b. If the function is shifted 2 units to the left then the x-intercepts become -6, -2, and 1. So the factors are
`(x+6)(x+2)^2(x-1)`.