Because they have the number 8 in common.
Answer:
Step-by-step explanation:
Given is an algebraic polynomial of degree 5.
![g(x) = 3x^5-2x^4+9x^3-x^2+12\\](https://tex.z-dn.net/?f=g%28x%29%20%3D%203x%5E5-2x%5E4%2B9x%5E3-x%5E2%2B12%5C%5C)
Here leading term is p=3 and constant term is q =12
Factors of p are ±1,±2,±3
Factors of q are ![\frac{±1,±2,±3,±4,±6,±12} \\](https://tex.z-dn.net/?f=%5Cfrac%7B%C2%B11%2C%C2%B12%2C%C2%B13%2C%C2%B14%2C%C2%B16%2C%C2%B112%7D%20%5C%5C)
Possible forms of p/q will be the same for any other polynomial of degree 5 with leading term =3 and constant term = 12
Hence any other polynomial
![g(x) = 3x^5+ax^4+bx^3+cx^2+12](https://tex.z-dn.net/?f=g%28x%29%20%3D%203x%5E5%2Bax%5E4%2Bbx%5E3%2Bcx%5E2%2B12)
will have same possible zeroes of p/q, when a,b,c are rational.
Hence any polynomial of this type would have the same possible rational roots.
The number 0.4 is written as a decimal.
Start with
![\dfrac{n}{5}=\dfrac{45}{75}](https://tex.z-dn.net/?f=%5Cdfrac%7Bn%7D%7B5%7D%3D%5Cdfrac%7B45%7D%7B75%7D)
Multiply both sides by 5:
![n = \dfrac{45\cdot 5}{75} = \dfrac{45}{15} = 3](https://tex.z-dn.net/?f=n%20%3D%20%5Cdfrac%7B45%5Ccdot%205%7D%7B75%7D%20%3D%20%5Cdfrac%7B45%7D%7B15%7D%20%3D%203)