Question

Which statement justifies that 3x2 − x − 5 multiplied by 2x2 − x − 3 obeys the closure property of multiplication?

The result 6x4 + x2 + 15 has a degree of 4.

The result 6x4 + x2 + 15 is a trinomial.

The result 6x4 − 5x3 − 18x2 + 8x + 15 is a polynomial.

The result 6x4 − 5x3 − 18x2 + 8x + 15 has a degree of 4.

Answer 1

The answer is C) The result 6x^4 - 5x^3 - 18x^2 + 8x + 15 is a polynomial.

Answer 2

Option C is correct.

Explanation:

Given Polynomials: 3x² - x - 5 and 2x² - x - 3

Closure property of multiplication.

States that if two polynomial multiplies then the result we get also is a polynomial.

So, first we find product of given polynomials.

( 3x² - x - 5 ) × ( 2x² - x - 3 )

= 3x² × ( 2x² - x - 3 ) - x × ( 2x² - x - 3 ) - 5 × ( 2x² - x - 3 )

`=6x^4 - 3x^3 - 9x^2 - 2x^3 +x^2+3x-10x^2+5x+15`

`=6x^4-5x^3-18x^2+8x+15`

Therefore, Option C is correct.