Question

The difference of two trinomials is x2 − 10x + 2. If one of the trinomials is 3x2 − 11x − 4, then which expression could be the other trinomial? 2x2 − x − 2 2x2 + x + 6 4x2 + 21x + 6 4x2 − 21x – 2

Answer 1

`4x^2-21x-2`

Explanation:

Given that:

Difference of two trinomials is
`x^2 - 10x + 2`

One of the two trinomials is
`3x^2 - 11x - 4`

To find:

The other trinomial = ?

Four options are:

`2x2 - x - 2 \\2x2 + x + 6 \\4x2 + 21x + 6\\ 4x2 - 21x - 2`

Solution:

Let the two trinomials be A and B.

Given A - B =
`x^2 - 10x + 2`

B =
`3x^2 - 11x - 4`

We have to find the other trinomial A.

A - B =
`x^2 - 10x + 2`

A - (
`3x^2 - 11x - 4`) =
`x^2 - 10x + 2`

`\Rightarrow` A =
`x^2 - 10x + 2` + (
`3x^2 - 11x - 4`)

`\Rightarrow` A =
`4x^2-21x-2`

So, the correct answer is
`4x^2-21x-2`.