Question

select the correct answer.
the difference of two trinomials is ( x^2 - 10x + 2 ). if one of the trinomials is ( 3x^2 - 11x - 4 ), then which expression could be the other trinomial?

• ( 2x^2 - x - 2 )
• ( 2x^2 + x + 6 )
• ( 4x^2 + 21x + 6 )
• ( 4x^2 - 21x - 2 )

Explanation:

Step1: Define variables for trinomials

Let the given trinomial be $A = 3x^2 - 11x - 4$, the unknown trinomial be $B$, and the difference be $D = x^2 - 10x + 2$. There are two cases: $A - B = D$ or $B - A = D$.

Step2: Solve for B in case 1 ($A - B = D$)

Rearrange to $B = A - D$. Substitute values:
$B = (3x^2 - 11x - 4) - (x^2 - 10x + 2) = 3x^2 - 11x - 4 - x^2 + 10x - 2 = 2x^2 - x - 2$. This matches the first option.

Step3: Verify case 2 (optional check)

For $B - A = D$, $B = A + D = (3x^2 -11x -4)+(x^2 -10x +2)=4x^2 -21x -2$, which is not needed as the first case gives a valid option.

Answer:

A. $2x^2 - x - 2$