Question

How do you write a polynomial in standard form, then classify it by degree and number of terms `4x(x – 5)(x + 6)`?

Answer 1

See a solution process below:

Explanation:

First, we can multiply the two terms in parenthesis on the right side of the expression. To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

`4x(color(red)(x) - color(red)(5))(color(blue)(x) + color(blue)(6))` becomes:

`4x((color(red)(x) xx color(blue)(x)) + (color(red)(x) xx color(blue)(6)) - (color(red)(5) xx color(blue)(x)) - (color(red)(5) xx color(blue)(6)))`

`4x(x^2 + 6x - 5x - 30)`

We can now combine like terms:

`4x(x^2 + (6 - 5)x - 30)`

`4x(x^2 + 1x - 30)`

`4x(x^2 + x - 30)`

Now, we can multiply each term within the parenthesis by the term outside the parenthesis:

`color(red)(4x)(x^2 + x - 30)`

`(color(red)(4x) xx x^2) + (color(red)(4x) xx x) - (color(red)(4x) xx 30)`

`4x^3 + 4x^2 - 120x`