Question

I asked before and didn’t get an answer I really don’t understand this thanks.

Which statement shows how two polynomials 4x^2 and x^2 + 3x + 7 demonstrate the closure property when multiplied?


A. 4x^3 + 12x^2 + 28x may or may not be a polynomial

B. 4x^3 + 12x^2 + 28x is a polynomial

C. 4x^4 + 12x^3 + 28x^2 may or may not be a polynomial

D. 4x^4 + 12x^3 + 28x^2 is a polynomial


Also I don't understand what it means by may or may not be polynomial. If someone could help out that'd be great

Answer 1

The answer is D, because that is what you should get when you multiply it out.

4x^2 times x^2 = 4x^4 because...

1) multiply the 4 and the one in front of the x on the second term = 4 then

2) multiply x^2 times x^2 to get x^4, not x^3, so you can immediately eliminate A and B to save time.

Now let's deal with the second part..."may or may not be" part

A polynomial is an expression with more than two algebraic terms

terms are like...
2x + 3y ---there's two terms there, eventhough the 2 and x are multiplied, it doesn't count (same with the 3 and y)
since it only have two terms, not more than two terms, it is called a binomial, not polynomial. I think that's what they mean by that

one term with a variable (y,x,and so on) is called a monomial

one term with no var is called a constant

there's many more but hope this gave you some help

Answer 2

D. 4x^4 + 12x^3 + 28x^2 is a polynomial

Multiply 4x^2 with x^2 + 3x + 7

4x^2(x^2) = 4x^4

4x^2(3x) = 12x^3

4x^2(7) = 28x^2

hope this helps