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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

Respuesta :

isyllus

Answer:

[tex]15x^3+18x^2-24x[/tex] is a polynomial.

B is correct

Step-by-step explanation:

Given: [tex]3x+6[/tex] and [tex]5x^2-4x[/tex]

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 [tex]3x+6[/tex] and [tex]5x^2-4x[/tex]

[tex]\Rightarrow (3x+6)(5x^2-4x)[/tex]

[tex]\Rightarrow 3x\cdot 5x^2-3x\cdot 4x+6\cdot 5x^2-4x\cdot 6[/tex]

[tex]\Rightarrow 15x^3-12x^2+30x^2-24x[/tex]

Combine the like terms

[tex]\Rightarrow 15x^3+18x^2-24x[/tex]

This is a polynomial with degree 3

Hence, The product of [tex]3x+6[/tex] and [tex]5x^2-4x[/tex] is a polynomial.

Answer:

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

Step-by-step explanation:

I took the test

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