Is there a faster way to do this besides simplifying each one?

Which equation is a quadratic equation?

y + 3 = −2x + 5 − 8x

y + 2x = −2x(4 − 3x) + 4

6x3 + y = (2x − 2)(3x + 7)

9x − y = (3x2 + 1)(5x − 1) + 4x

Question

Is there a faster way to do this besides simplifying each one?

Which equation is a quadratic equation?

 y + 3 = −2x + 5 − 8x

 y + 2x = −2x(4 − 3x) + 4

 6x3 + y = (2x − 2)(3x + 7)

 9x − y = (3x2 + 1)(5x − 1) + 4x

ja1 · Answer

Anyone? It is a pretty straight forward question :P

ja1 · Answer

Lalalalalala......

amistre64 · Answer

highest degree for x is 2 for a quadratic

mathstudent55 · Answer

All you need to do is look carefully.
You must check two things.
If when distributing you get a x^2 term, there is a potential for a quadratic.
Then you need to make sure there isn't another x^2 term that will cancel the first one out.

amistre64 · Answer

(x)(x) is quadratic

mathstudent55 · Answer

For example, the first equation, choice A, has no products of x and x. Every term is first degree, so it cannot be a quadratic.

ja1 · Answer

OHHH ok I see, so if it has 1 x^2 there is a remote possibility?

mathstudent55 · Answer

Now look at choice B. When you distribute on the right side, (-2x)(-3x) = 6x^2. That is quadratic. Since there is no other term anywhere that is quadratic that could cancel this one out, and there is no other higher degree than 2, then this is a quadratic equation.

mathstudent55 · Answer

Yes.

ja1 · Answer

Ah I see, well this will save me many precious minutes from my life <_< thanks @mathstudent55 ^,^

mathstudent55 · Answer

Now look at choice C. Since it starts out with an x^3 term, there is a chance it's a 3rd degree polynomial, and not quadratic. On the right side, there is (2x)(3x) which is 6x^2, but since the highest term is 3rd degree and does not get cancelled, it's a 3rd degree polynomial and not a quadratic.

ja1 · Answer

Ah ok, so there is no chance the ^3 will be cancelled out so that is automatically out of the question.

mathstudent55 · Answer

Now look at choice D. What do you see on the right side? Meaning, what is the highest degree you'll get on the right side after distributing?

ja1 · Answer

x^3

ja1 · Answer

3x^2 * 5x = 15^3

ja1 · Answer

right?

mathstudent55 · Answer

Correct. You get 3rd degree on the right side. There is no other 3rd degree term anywhere else that could cancel this one, so it's a 3rd degree polynomial equation, not quadratic.

ja1 · Answer

HUZZAH you have truly helped me C: thanks a bunch