Question

What is the standard form of # y=(3x – 4) (2x – 1) (x – 2) #?

Answer 1

`6x^3-23x^2+26x-8`

Explanation:

`(3x-4)(2x-1)(x-2)`

Writing this in Standard Form (of a polynomial) means that the terms are in order from highest to lowest degree (those tiny little numbers to the right of the `x`).

`(3x-4)(2x-1)(x-2)`

a) Multiply `(3x-4)` and `(2x-1)`*:
`(6x^2-3x-8x+4)(x-2)`

• I combined (added) `-3x` and `-8x` to get `-11x`

b) Multiply `(6x^2-11x+4)` and `(x-2)`:
`6x^3-11x^2+4x-12x^2+6x+16x-8`

c) Rearrange terms into Standard Form:
`6x^3-11x^2-12x^2+4x+6x+16x-8`

d) Simplify:
`6x^3-23x^2+26x-8`

Notes:

• Due to the Associative Property of Multiplication, you can multiply these in any order you want to, I just usually go form left to right.
• I said to Multiply but this could be called FOILing or Distributing by your teacher
• You can always check the answer by factor it back out again because it is entirely possible that I had a multiplication, addition, or subtraction error along the way.