Question

subtract these polynomials.

$(6x^3 - 4x + 5) - (3x^3 - 5x^2 + 6x - 2) =$

a. $3x^3 - 5x^2 + 2x + 7$

b. $3x^3 - 5x^2 - 10x + 7$

c. $3x^3 + 5x^2 + 2x + 7$

d. $3x^3 + 5x^2 - 10x + 7$

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:
$$(6x^3 - 4x + 5) - (3x^3 - 5x^2 + 6x - 2) = 6x^3 - 4x + 5 - 3x^3 + 5x^2 - 6x + 2$$

Step2: Combine like terms

• For the \(x^3\) terms: \(6x^3 - 3x^3 = 3x^3\)
• For the \(x^2\) terms: \(0x^2 + 5x^2 = 5x^2\) (since there's no \(x^2\) term in the first polynomial, we consider its coefficient as 0)
• For the \(x\) terms: \(-4x - 6x = -10x\)
• For the constant terms: \(5 + 2 = 7\)

Putting it all together, we get:
$$3x^3 + 5x^2 - 10x + 7$$

Answer:

D. \(3x^3 + 5x^2 - 10x + 7\)