Question

question 1 of 10
subtract these polynomials.
(3x² + 2x + 4) − (x² + 2x + 1) =
a. 2x² + 4x + 5
b. 2x² + 3
c. 2x² + 4x + 3
d. 2x² + 5

Explanation:

Step1: Distribute the subtraction

To subtract the polynomials, we first distribute the negative sign to the second polynomial:
$(3x^2 + 2x + 4) - (x^2 + 2x + 1) = 3x^2 + 2x + 4 - x^2 - 2x - 1$

Step2: Combine like terms

• For $x^2$ terms: $3x^2 - x^2 = 2x^2$
• For $x$ terms: $2x - 2x = 0$ (they cancel out)
• For constant terms: $4 - 1 = 3$

Putting it all together, we get $2x^2 + 0x + 3 = 2x^2 + 3$.

Answer:

B. $2x^2 + 3$