Question

select the correct answer from each drop-down menu.

consider the expressions given below.

a. \\(2x^3 - x^2 - 6x\\)
b. \\(2x^3 + 8x + 4\\)
c. \\(3x^4 + x^2 + x - 7\\)
d. \\(3x^4 - 3x^2 + 5x - 7\\)

for each expression below, select the letter that corresponds to the equivalent expression from the given list.

• \\((4x^3 - 4 + 7x) - (2x^3 - x - 8)\\) is equivalent to expression choose an answer
• \\((-3x^2 + x^4 + x) + (2x^4 - 7 + 4x)\\) is equivalent to expression choose an answer
• \\((x^2 - 2x)(2x + 3)\\) is equivalent to expression choose an answer

Explanation:

⚡ Using what you learned: adding and subtracting polynomials · multiplying polynomials

Step 1: Simplify the first expression

Evaluate the subtraction:

$$ (4x^3 - 4 + 7x) - (2x^3 - x - 8) $$

Distribute the negative sign:

$$ 4x^3 - 4 + 7x - 2x^3 + x + 8 $$

Group and combine like terms:

$$ (4x^3 - 2x^3) + (7x + x) + (-4 + 8) $$

$$ 2x^3 + 8x + 4 $$

This matches expression B.

Step 2: Simplify the second expression

Evaluate the addition:

$$ (-3x^2 + x^4 + x) + (2x^4 - 7 + 4x) $$

Group and combine like terms in descending order of powers:

$$ (x^4 + 2x^4) - 3x^2 + (x + 4x) - 7 $$

$$ 3x^4 - 3x^2 + 5x - 7 $$

This matches expression D.

Step 3: Simplify the third expression

Evaluate the multiplication:

$$ (x^2 - 2x)(2x + 3) $$

Expand using the distributive property (FOIL):

$$ x^2(2x) + x^2(3) - 2x(2x) - 2x(3) $$

$$ 2x^3 + 3x^2 - 4x^2 - 6x $$

Combine like terms:

$$ 2x^3 - x^2 - 6x $$

This matches expression A.

Answer:

• \( (4x^3 - 4 + 7x) - (2x^3 - x - 8) \) is equivalent to expression B
• \( (-3x^2 + x^4 + x) + (2x^4 - 7 + 4x) \) is equivalent to expression D
• \( (x^2 - 2x)(2x + 3) \) is equivalent to expression A