Question

The difference of two trinomials is x2 - 10x + 2. If one of the trinomials is 3x? - 11x - 4, then which expression could be the othe
trinomial?
0 27-x-2
2x2 + x + 6
4x2 + 21x + 6
0
4x2
21x-2

Answer 1

Answer:

$2x^2-x-6$

or

$4x^2-21x-2$

Step-by-step explanation:

The difference of two trinomials $P(x)$ and $Q(x)$ is $x^2 - 10x + 2.$ This means that

$P(x)-Q(x)=x^2-10x+2$

or

$Q(x)-P(x)=x^2-10x+2$

If one of the trinomials is $P(x)=3x^2-11x - 4,$ then

$(3x^2-11x-4)-Q(x)=x^2-10x+2$

or

$Q(x)-(3x^2-11x-4)=x^2-10x+2$

1. If $(3x^2-11x-4)-Q(x)=x^2-10x+2,$ then

$Q(x)=(3x^2-11x-4)-(x^2-10x+2)\\ \\Q(x)=(3x^2-x^2)+(-11x+10x)+(-4-2)\\ \\Q(x)=2x^2-x-6$

2. If $Q(x)-(3x^2-11x-4)=x^2-10x+2,$ then

$Q(x)=(x^2-10x+2)+(3x^2-11x-4)\\ \\Q(x)=(x^2+3x^2)+(-10x-11x)+(2-4)\\ \\Q(x)=4x^2-21x-2$