Question

select the correct answer.

the sum of two trinomials is (6x^2 - 5x + 4). if one of the trinomials is (4x^2 + 3x - 2), then what is the other trinomial?

• (10x^2 + 2x - 2)
• (10x^2 + 8x - 6)
• (2x^2 - 2x + 2)
• (2x^2 - 8x + 6)

Explanation:

⚡ Using what you learned: adding and subtracting polynomials

Step 1: Set up the equation

Let \( P(x) \) be the unknown trinomial.

$$ (4x^2 + 3x - 2) + P(x) = 6x^2 - 5x + 4 $$

$$ P(x) = (6x^2 - 5x + 4) - (4x^2 + 3x - 2) $$

Step 2: Distribute the negative sign

$$ P(x) = 6x^2 - 5x + 4 - 4x^2 - 3x + 2 $$

Step 3: Combine like terms

$$ P(x) = (6x^2 - 4x^2) + (-5x - 3x) + (4 + 2) $$

$$ P(x) = 2x^2 - 8x + 6 $$

Answer:

\( 2x^2 - 8x + 6 \)