Question

Use synthetic division to find the quotient and remainder of (3
`x^(4)`-8
`x^(3)`+9x+5)+(x-2)

Answer 1

How to get answer:

`\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\\=3x^4-8x^3+9x+5+x-2\\Group\:like\:terms\\=3x^4-8x^3+9x+x+5-2\\\mathrm{Add\:similar\:elements:}\:9x+x=10x\\=3x^4-8x^3+10x+5-2\\\mathrm{Add/Subtract\:the\:numbers:}\:5-2=3\\=3x^4-8x^3+10x+3`

Answer 2

For this case we have a polynomial division.

A term of the quotient must be found step by step to eliminate the terms of the dividend.

The final result must comply with:

`P (x) = Q (x) * D (x) + R (x)\\`

Where:

P (x) is the dividend

Q (x) is the quotient

D (x) is the divisor

R (x) is the remainder

Answer:

See attached image