Question

(b) $(3x^2 - 5x + 3) + (x^2 + 2x - 4)$

Explanation:

Step1: Remove the parentheses

To add the two polynomials, we first remove the parentheses. Since there are no negative signs outside the parentheses to distribute (other than the existing signs in the polynomials), we can simply write the terms as they are: $3x^{2}-5x + 3+x^{2}+2x - 4$.

Step2: Combine like terms

• For the $x^{2}$ terms: $3x^{2}+x^{2}=(3 + 1)x^{2}=4x^{2}$.
• For the $x$ terms: $-5x+2x=(-5 + 2)x=-3x$.
• For the constant terms: $3-4=-1$.

Putting these combined like terms together, we get $4x^{2}-3x - 1$.

Answer:

$4x^{2}-3x - 1$