Question

Urgent! The polynomials `ax^3-3x^2+2x-3` and `ax^2-5x+a` when divided by `x-2` leave remainders of `p` and `q` respectively. Find the value of `a` if `p=3q`. How? Urgent thanks!

Answer 1

`a=19/7,p=75/7,q=25/7`

Explanation:

Calling

`f_1(x)=ax^3-3x^2+2x-3`
`f_2(x)=ax^2-5x+a`

we know that

`f_1(x)=q_1(x)(x-2)+p` and
`f_2(x)=q_2(x)(x-2)+q`

so

`f_1(2) = 8a-12+4-3=p`
`f_2(2)=4a-10+a=q` and also
`p=3q`

Solving

`{(8a-11=p),(5a-10=q),(p=3q):}`

we obtain

`a=19/7,p=75/7,q=25/7`