Question

What is the standard form of `y= (3x-5)(x+1)(x-2)`?

Answer 1

`color(blue)(y = 3x^3-8x^2-x+10)`

Explanation:

We have the factors given to us

`y = (3x-5)(x + 1) (x-2)`

We will focus on the factors on the right hand side of the equation.

We can use the FOIL Method to multiply the binomials .

Multiply the `color(red)(F)`irst terms.
Multiply the `color(red)(O)`uter terms.
Multiply the `color(red)(I)`nner terms.
Multiply the `color(red)(L)`ast terms.

We will keep the first factor as it is, but multiply the last two factors to get:

`(3x-5)(x^2 - 2x + x - 2)`

`rArr(3x-5)(x^2 - x - 2)`

Net we will multiply these two factors to get:

`3x^3-3x^2-6x-5x^2+5x+10`

`rArr 3x^3 - 8x^2 - x +10`

So, we have

`color(blue)(y = 3x^3 - 8x^2 - x +10)`

which is the required polynomial in standard form.

I hope that helps.