An example of an exponential function is the growth of bacteria.
The zeros of the polynomial are <span>1, 2, -2 and -3, so this polynomial must have at least one of each of these factors:
(x-1), (x-2), (x-(-2)), and (x-(-3)); rewriting: </span>(x-1), (x-2), (x+2), and (x+3).
Thus, any such polynomial must have a factor (x-1)(x-2)(x+2)(x+3).
The simplest such polynomial we can think of, is p(x)=(x-1)(x-2)(x+2)(x+3).
To write in standard form, lets first multiply the factors two by two as follows:
![(x-2)(x+2)=x^2-4](https://tex.z-dn.net/?f=%28x-2%29%28x%2B2%29%3Dx%5E2-4)
by the difference of squares formula,
![(x-1)(x+3)=x^2+2x-3](https://tex.z-dn.net/?f=%28x-1%29%28x%2B3%29%3Dx%5E2%2B2x-3)
.
Next, we multiply our results:
![(x^2-4)(x^2+2x-3)=x^2(x^2+2x-3)-4(x^2+2x-3)](https://tex.z-dn.net/?f=%28x%5E2-4%29%28x%5E2%2B2x-3%29%3Dx%5E2%28x%5E2%2B2x-3%29-4%28x%5E2%2B2x-3%29)
![=x^4+2x^3-3x^2-4x^2-8x+12=x^4+2x^3-7x^2-8x+12](https://tex.z-dn.net/?f=%3Dx%5E4%2B2x%5E3-3x%5E2-4x%5E2-8x%2B12%3Dx%5E4%2B2x%5E3-7x%5E2-8x%2B12)
.
Answer:
Answer:
the roots are 5 and -3
Step-by-step explanation:
factorise and you should get (n+3)(n-5)
Answer:
answer is Commutative Property
Step-by-step explanation: