Final answer:
To make the given statement true, we combine like terms and set coefficients equal to those on the right side of the equation, yielding the solutions: a = 6, b = 2, and c = -1.
Step-by-step explanation:
To find the values of a, b, and c that make the statement true, we need to combine like terms in the given expression:
(3x² + ax - 3) + (bx² - 3x + 5) - (4x² + 2x - c) = x² + x + 1.
First, we combine the x² terms:
3x² + bx² - 4x² = (3+b-4)x².
Next, combine the x terms:
ax - 3x - 2x = (a-3-2)x.
Now, combine the constant terms:
-3 + 5 + c = c + 2.
To find the equivalent polynomial, set the coefficients equal to those of x² + x + 1:
(3+b-4)x² = 1x² → b = 2.
(a-3-2)x = 1x → a = 6.
c + 2 = 1 → c = -1.
So, the values that make the statement true are a = 6, b = 2, and c = -1.