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

Answer:

$4x^2-21x-2$

Step-by-step 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 $4x^2-21x-2$.