Consider the product (2x−x3)(−3x4−7x2). Which of the following is the correct expression when each term of the first polynomial is distributed onto the second polynomial?(1 point)%0D%0AResponses%0D%0A%0D%0A2x(−3x4−7x2)+x3(−3x4−7x2)%0D%0A2 x left parenthesis negative 3 x superscript 4 baseline minus 7 x squared right parenthesis plus x cubed left parenthesis negative 3 x superscript 4 baseline minus 7 x squared right parenthesis%0D%0A%0D%0A2x(−3x4)−x3(−7x2)%0D%0A2 x left parenthesis negative 3 x superscript 4 baseline right parenthesis minus x cubed left parenthesis negative 7 x squared right parenthesis%0D%0A%0D%0A2x(−3x4−7x2)−x3(−3x4−7x2)%0D%0A2 x left parenthesis negative 3 x superscript 4 baseline minus 7 x squared right parenthesis minus x cubed left parenthesis negative 3 x superscript 4 baseline minus 7 x squared right parenthesis%0D%0A%0D%0A2x(−x3−3x4−7x2)

Answer 1

To distribute the first polynomial \((2x - x^3)\) onto the second polynomial \((-3x^4 - 7x^2)\), we need to apply the distributive property, multiplying each term in the first polynomial by each term in the second polynomial.

The steps are as follows:

1. Distribute \(2x\) to each term in \((-3x^4 - 7x^2)\): \[ 2x \cdot (-3x^4) + 2x \cdot (-7x^2) = -6x^5 - 14x^3 \]

2. Distribute \(-x^3\) to each term in \((-3x^4 - 7x^2)\): \[ -x^3 \cdot (-3x^4) + -x^3 \cdot (-7x^2) = 3x^7 + 7x^5 \]

Putting it all together, you get: \[ -6x^5 - 14x^3 + 3x^7 + 7x^5 \]

However, since the question asks for the expression after distribution without combining like terms, the correct representation for distributing each term of \((2x - x^3)\) onto \((-3x^4 - 7x^2)\) can be shown as: \[ 2x(-3x^4 - 7x^2) - x^3(-3x^4 - 7x^2) \]

Thus, the correct answer is: \[ 2x(-3x^4 - 7x^2) - x^3(-3x^4 - 7x^2) \]

In the provided response options, the correct choice is: 2 x left parenthesis negative 3 x superscript 4 baseline minus 7 x squared right parenthesis minus x cubed left parenthesis negative 3 x superscript 4 baseline minus 7 x squared right parenthesis.