Question

How do you use synthetic division to divide `5x^77 - 4x^60 + 2x^43 + 6x^30 - 4x^19 + 2` divided by x - 1?

Answer 1

That's going to take you forever.

Explanation:

Here's a link to a great video explaining Synthetic Division Synthetic Division-Khan Academy. Also, whoever assigned you that problem must wish you hell.

Answer 2

Also, use Wolfram Alpha to check your work ...

Explanation:

`5 x^76+5 x^75+5 x^74+5 x^73+5 x^72+5 x^71+5 x^70+5 x^69+5 x^68+5 x^67+5 x^66+5 x^65+5 x^64+5 x^63+5 x^62+5 x^61+5 x^60+x^59+x^58+x^57+x^56+x^55+x^54+x^53+x^52+x^51+x^50+x^49+x^48+x^47+x^46+x^45+x^44+x^43+3 x^42+3 x^41+3 x^40+3 x^39+3 x^38+3 x^37+3 x^36+3 x^35+3 x^34+3 x^33+3 x^32+3 x^31+3 x^30+9 x^29+9 x^28+9 x^27+9 x^26+9 x^25+9 x^24+9 x^23+9 x^22+9 x^21+9 x^20+9 x^19+5 x^18+5 x^17+5 x^16+5 x^15+5 x^14+5 x^13+5 x^12+5 x^11+5 x^10+5 x^9+5 x^8+5 x^7+5 x^6+5 x^5+5 x^4+5 x^3+5 x^2+5 x+7/(x-1)+5`

Source:
http://tinyurl.com/q96x3lo

Answer 3

You can use the remainder theorem to determine the remainder as:

`5-4+2+6-4+2 = 7`

As for the quotient, I would not use synthetic division...

Explanation:

Use:

`x^N-1 = (x-1)sum_(n=0)^(N-1) x^n`

Hence:

`5x^77-4x^60+2x^43+6x^30-4x^19+2`

`=5(x^77-1)-4(x^60-1)+2(x^43-1)+6(x^30-1)-4(x^19-1)+7`

`=(x-1)(sum_(n=0)^76 5x^n - sum_(n=0)^59 4x^n + sum_(n=0)^42 2x^n + sum_(n=0)^29 6x^n - sum_(n=0)^18 4x^n) + 7`

`=(x-1)(sum_(n=60)^76 5x^n + sum_(n=43)^59 x^n + sum_(n=30)^42 3x^n + sum_(n=19)^29 9x^n + sum_(n=0)^18 5x^n) + 7`