Question

subtract these polynomials.
$(3x^2 + 3x + 3) - (x^2 + 2x + 3) =$
a. $2x^2 + x + 6$
b. $2x^2 + 5x + 6$
c. $2x^2 + x$
d. $2x^2 + 5x$

Explanation:

Step1: Distribute the negative sign

To subtract the second polynomial from the first, we distribute the negative sign to each term in the second polynomial:
$$(3x^2 + 3x + 3) - x^2 - 2x - 3$$

Step2: Combine like terms

• For the \(x^2\) terms: \(3x^2 - x^2 = 2x^2\)
• For the \(x\) terms: \(3x - 2x = x\)
• For the constant terms: \(3 - 3 = 0\)

Putting it all together, we get \(2x^2 + x + 0 = 2x^2 + x\)

Answer:

C. \(2x^2 + x\)