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: Let the other trinomial be $A$.

Set up the equation: $(3x^{2}-11x - 4)-A=x^{2}-10x + 2$ or $A-(3x^{2}-11x - 4)=x^{2}-10x + 2$. Solving the first - case for $A$ gives $A=(3x^{2}-11x - 4)-(x^{2}-10x + 2)$.

Step2: Expand the right - hand side.

$A = 3x^{2}-11x - 4-x^{2}+10x - 2$.

Step3: Combine like terms.

$A=(3x^{2}-x^{2})+(-11x + 10x)+(-4 - 2)=2x^{2}-x - 6$. Solving the second - case for $A$ gives $A=(3x^{2}-11x - 4)+(x^{2}-10x + 2)$.

Step4: Expand and combine like terms for the second - case.

$A=3x^{2}-11x - 4+x^{2}-10x + 2=(3x^{2}+x^{2})+(-11x-10x)+(-4 + 2)=4x^{2}-21x - 2$.

Answer:

D. $4x^{2}-21x - 2$