What in the world is a second-degree polynomial?

Question

Ok, here's the question from the book:

Factor the following expression and include a second degree expression as a factor.

16x^3 + 54y^6

What the heck are they talking about? What exactly do they want me to do? I've never heard the term, and they don't give any examples. Anyone know what they're talking about?

Answer 1

A second degree polynomial is one where the highest power of any term is 2. For this example, the second degree polynomial will actually be second degree because of the y term, not the x. First, remove a factor of 2:

2(8x³+27y⁶)

Now, note that this is the sum of cubes:

2((2x)³+(3y²)³)

Factor accordingly:

2 (2x+3y²) (4x² - 6xy² + 9y⁴)

The second expression is of degree 2, and the third is of degree 4. All of these expressions are irreducible, so we are done.

Answer 2

In a second-degree polynomial in x the highest power of x is x^2. So you are supposed to factor the expression into the form (a*x^2 + b*y*n)*(c*x + d*y^m). Also, it could be of the form (a*x^r + b*y^2)*(c*x^s + d*y^4). There are other possibilities as well.

Answer 3

There are an infinite style of genuine numbers obtainable. Given any genuine extensive style, you may upload a million to it to get yet another one. The set of genuine numbers has no end. As such, no computing gadget will ever be waiting to checklist all of them. an infinite style of issues takes an infinite volume of time to technique, besides the undeniable fact that quickly you do it. no count number what proportion numbers the computing gadget listed, there could continuously be extra.

Answer 4

16x^3 + 54y^6 = 2^4x^3 + 2(3^3)y^6
= 2(2x)^3 + 2(3y^2)^3