Question

What is the standard form of a polynomial `(3x+4)(5x-9)`?

Answer 1

See a solution process below:

Explanation:

To write this polynomial in standard form we must multiply these two terms by multiplying each individual term in the left parenthesis by each individual term in the right parenthesis.

`(color(red)(3x) + color(red)(4))(color(blue)(5x) - color(blue)(9))` becomes:

`(color(red)(3x) xx color(blue)(5x)) - (color(red)(3x) xx color(blue)(9)) + (color(red)(4) xx color(blue)(5x)) - (color(red)(4) xx color(blue)(9))`

`15x^2 - 27x + 20x + 36`

We can now combine like terms:

`15x^2 + (-27 + 20)x + 36`

`15x^2 + (-7)x + 36`

`15x^2 - 7x + 36`