Question

select the correct answer.

which expression is equivalent to this polynomial?
\\6x^2 + 10x - 56\\

• \\(4(x - 4) - 2(3x^2 + 3x - 20)\\)
• \\((3x^2 + 5x - 28) + (3x^2 - 5x - 28)\\)
• \\(4(x - 4) + 2(3x^2 + 3x - 20)\\)
• \\((3x^2 + 5x - 28) - (3x^2 + 5x - 28)\\)

Explanation:

⚡ Using what you learned: adding and subtracting polynomials

Step 1: Analyze the target polynomial

The target expression is:

$$ 6x^2 + 10x - 56 $$

Step 2: Evaluate Option 1

$$ 4(x - 4) - 2(3x^2 + 3x - 20) $$

$$ = 4x - 16 - 6x^2 - 6x + 40 $$

$$ = -6x^2 - 2x + 24 $$

Step 3: Evaluate Option 2

$$ (3x^2 + 5x - 28) + (3x^2 - 5x - 28) $$

$$ = 3x^2 + 3x^2 + 5x - 5x - 28 - 28 $$

$$ = 6x^2 - 56 $$

Step 4: Evaluate Option 3

$$ 4(x - 4) + 2(3x^2 + 3x - 20) $$

$$ = 4x - 16 + 6x^2 + 6x - 40 $$

$$ = 6x^2 + 10x - 56 $$

Answer:

\( 4(x - 4) + 2(3x^2 + 3x - 20) \)