Question

Which statement shows how two polynomials 5x − 6 and 6x + 2 demonstrate the closure property when multiplied? (1 point)

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

The statement shows how two polynomials 5x − 6 and 6x + 2 demonstrate the closure property when multiplied

A: 30x² − 26x − 12 may or may not be a polynomial

B: 30x² − 11x − 12 may or may not be a polynomial

C: 30x² − 26x − 12 is a polynomial

D: 30x² − 11x − 12 is a polynomial

EVALUATION

Here the given two polynomials are 5x − 6 and 6x + 2

Multiplying we get

(5x − 6) × ( 6x + 2)

$\sf{ = 5x(6x + 2) - 6(6x + 2)}$

$\sf{ = 30 {x}^{2} + 10x - 36x - 12}$

$\sf{ = 30 {x}^{2} - 26x - 12}$

Here 5x − 6 and 6x + 2 are polynomials

Since the product of two polynomials is always a polynomial

So 30x² − 26x − 12 is a polynomial

FINAL ANSWER

Hence the correct option is

C : 30x² − 26x − 12 is a polynomial

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