Question

add $(5x^4 - 9x^2 + 3x - 11) + (2x^2 - 7x^3 + 18)$

a) $5x^4 - 2x^3 - 8x^2 + 5x - 7$

b) $7x^6 - 2x^5 + 21x - 11$

c) $5x^4 - 7x^3 - 7x^2 + 3x + 7$

d) none of these

e) $12x^4 - 7x^2 + 7$

Explanation:

Step1: Remove parentheses

To add the two polynomials, we first remove the parentheses: \( (5x^4 - 9x^2 + 3x - 11)+(2x^2 - 7x^3 + 18)=5x^4 - 9x^2 + 3x - 11 + 2x^2 - 7x^3 + 18 \)

Step2: Combine like terms

• For \( x^4 \) term: only \( 5x^4 \)
• For \( x^3 \) term: only \( -7x^3 \)
• For \( x^2 \) terms: \( -9x^2+2x^2=-7x^2 \)
• For \( x \) term: only \( 3x \)
• For constant terms: \( -11 + 18 = 7 \)

So combining all like terms, we get \( 5x^4-7x^3-7x^2 + 3x+7 \)

Step3: Match with options

Now we check the options:

• Option A: \( 5x^4-2x^3-8x^2 + 5x-7 \) does not match.
• Option B: \( 7x^6-2x^5 + 21x-11 \) does not match.
• Option C: \( 5x^4-7x^3-7x^2 + 3x + 7 \) matches our result.
• Option D: Since option C is correct, D is incorrect.
• Option E: \( 12x^4-7x^2 + 7 \) does not match.

Answer:

C. \( 5x^4 - 7x^3 - 7x^2 + 3x + 7 \)