Question

Which statement shows how two polynomials 3x + 6 and 5x2 − 4x demonstrate the closure property when multiplied?

A: 15x3 + 18x2 − 24x may or may not be a polynomial
B: 15x3 + 18x2 − 24x is a polynomial
C: 15x3 + 42x2 − 24x may or may not be a polynomial
D: 15x3 + 42x2 − 24x is a polynomial

Answer 1

B: 15x3+18x2-24x is a polynomial

Explanation:

I took the test

Answer 2

`15x^3+18x^2-24x` is a polynomial.

B is correct

Explanation:

Given:
`3x+6` and
`5x^2-4x`

There are two polynomial with each has two term.

Using closure property multiplied both polynomial.

• If multiply two polynomial then result must be a polynomial with higher degree of previous two.

Product of
`3x+6` and
`5x^2-4x`

`\Rightarrow (3x+6)(5x^2-4x)`

`\Rightarrow 3x\cdot 5x^2-3x\cdot 4x+6\cdot 5x^2-4x\cdot 6`

`\Rightarrow 15x^3-12x^2+30x^2-24x`

Combine the like terms

`\Rightarrow 15x^3+18x^2-24x`

This is a polynomial with degree 3

Hence, The product of
`3x+6` and
`5x^2-4x` is a polynomial.