Question

subtract these polynomials.

$(3x^7 + 6x^4 - 5x + 7) - (6x^4 - 5x^3 + 7) =$

a. $3x^7 + 6x^4 - 5x^3 - 5x$

b. $3x^7 - 5x^3 - 5x$

c. $3x^7 + 5x^3 - 5x$

d. $3x^7 + 6x^4 + 5x^3 - 5x$

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:
$$(3x^7 + 6x^4 - 5x + 7) - 6x^4 + 5x^3 - 7$$

Step2: Combine like terms

• For the \(x^7\) term: \(3x^7\) (no other \(x^7\) terms to combine with)
• For the \(x^4\) terms: \(6x^4 - 6x^4 = 0\)
• For the \(x^3\) term: \(5x^3\) (no other \(x^3\) terms to combine with initially, but from the distributed negative, we have \(+5x^3\))
• For the \(x\) term: \(-5x\) (no other \(x\) terms to combine with)
• For the constant terms: \(7 - 7 = 0\)

Putting it all together, we get:
$$3x^7 + 5x^3 - 5x$$

Answer:

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