Question

The difference between two trinomials is 5x2 + 11x − 16. If one of the trinomials is 3x2 − 2x + 7, then which expression could be the other trinomial?

Answer 1

`2x^2+13x-23`

Explanation:

The first trinomial is

`3x^2-2x+7`

Let the other trinomial be P.

Then

`P+3x^2-2x+7=5x^2+11x-16`

We make P the subject to obtain,

`P=5x^2-3x^2+11x+2x-16-7`

We simplify to obtain,

`P=2x^2+13x-23`

Hence the other trinomial is
`2x^2+13x-23`

Answer 2

other trinomial is ( 8x² + 9x - 9 )

Explanation:

The difference between two trinomials is 5x² + 11x - 16.

If one of the trinomials is 3x² - 2x + 7 then we have to find the other trinomial.

Let the other trinomial is T.

Then T - ( 3x² - 2x + 7 ) = 5x² + 11x - 16

T = ( 5x² + 11x - 16 ) + ( 3x² - 2x + 7 )

= 5x² + 11x - 16 + 3x² - 2x + 7

= ( 5x² + 3x² ) + ( 11x - 2x ) - ( 16 - 7 )

= 8x² + 9x - 9

Therefore, other trinomial is ( 8x² + 9x - 9 )