Question

Find the product of (4x − 3)(2x2 − 7x + 1).

8x3 − 22x2 + 17x− 3

8x3 + 8x2 + 4x − 3

8x3 − 34x2 + 25x − 3

8x3 − 42x2 + 25x − 3

Find the product of 2x4(4x2 + 3x + 1).

8x6 + 6x5 + 2x4

8x8 + 3x4 + 2x4

2x4 + 6x5 + 8x6

6x6 + 5x5 + 3x4



Which statement shows that when two polynomials 4x + 6 and 2x2 − 8x demonstrates the closure property when multiplied?

8x3 − 20x2 − 48x is a polynomial

8x3 − 20x2 + 48x may or may not be a polynomial

8x2 − 32x2 − 14x is a polynomial

8x3 − 32x2 + 14x may or may not be a polynomial

Answer 1

1. The correct answer among the choices provided is 8x3 − 34x2 + 25x − 3.
2. The correct answer among the choices provided is 8x6 + 6x5 + 2x4.
3. The correct answer among the choices provided is 8x3 − 20x2 − 48x. It is a polynomial.

Answer 2

The correct answers are:

(1)
`~8x^3 -34x^2 + 25x -3 ~~` (Option C)

(2)
`~ 8x^(6) + 6x^(5) + 2x^4 ~~` (Option A)

(3)
`~ 8x^3 - 20x^2-48x ~~` is a polynomial (Option A)

Explanations:

(1) Given Expression:

`(4x-3)(2x^2-7x + 1)`

Now simplify as follows:

`4x(2x^2 - 7x + 1) - 3(2x^2 - 7x + 1) \\8x^3 - 28x^2 + 4x - 6x^2 + 21x - 3 \\8x^3 -34x^2 + 25x -3`

Therefore, the correct answer is
`8x^3 -34x^2 + 25x -3` (Option C)

(2) Given Expression:

`2x^4(4x^2 + 3x + 1)`

Now simplify as follows:

`2x^4(4x^2 + 3x + 1) \\2x^4(4x^2) + 2x^4(3x) + 2x^4(1) \\8x^((4+2)) + 6x^((4+1)) + 2x^4 \\8x^(6) + 6x^(5) + 2x^4`

Therefore, the correct answer is
`8x^(6) + 6x^(5) + 2x^4` (Option A)

(3) Given Data:

Polynomial one: 4x + 6

Polynomial two:
`2x^2-8x`

First multiply both polynomials:

`(4x + 6) * (2x^2-8x) \\(4x) * (2x^2-8x) + (6) * (2x^2-8x) \\8x^3-32x^2+12x^2-48x \\8x^3-20x^2-48x`

Now as we can see, if we multiply two polynomials, the resultant expression is also a polynomial. Therefore, it does demonstrate the closure property (closed set). Hence, the correct answer is
`8x^3-20x^2-48x ~~` (Option A)