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?

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

Explanation:

Step1: Define the unknown trinomial

Let the other trinomial be $ax^2 + bx + c$.

Step2: Set up the sum equation

$ (4x^2 + 3x - 2) + (ax^2 + bx + c) = 6x^2 - 5x + 4 $

Step3: Combine like terms

$ (4+a)x^2 + (3+b)x + (-2+c) = 6x^2 -5x +4 $

Step4: Solve for coefficients

• $4+a=6 \Rightarrow a=2$
• $3+b=-5 \Rightarrow b=-8$
• $-2+c=4 \Rightarrow c=6$

Answer:

2x² - 8x + 6