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

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.

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IsrarAwan IsrarAwan · Answer 2 · 2018-07-29T19:44:52-04:00

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)