Question

What is the standard form of `y= (x-3)(x^3-5)*3x^4-5`?

Answer 1

In standard form
`color(white)("XXX")y=3x^8-9x^7-15x^5+45x^4-5`

Explanation:

`underbrace((x-3)(x^3-5)) * 3x^4-5`

`= underbrace((x^4-5x-3x^3+15) * (3x^4))-5`

`=underbrace((3x^8-15x^5-9x^7+45x^4)-5)`

`=3x^8-15x^5-9x^7+45x^4-5`

To write this in standard form the terms must be arranged in descending degree (where degree is the sum of all variable exponents in the term)
#{: (ul("term"),color(white)("xxxx"),ul("degree")), (3x^8,,8), (-15x^5,,5), (-9x^7,,7),(45x^4,,4), (-5,,0) :}#

Arranged in decreasing degree order:
`y=3x^8-9x^7-15x^5+45x^4-5`