Question

which polynomial represents the difference below?
$12x^3 + 7x + 3 - (3x^7 + 4x)$
a. $-3x^7 + 12x^3 + 11x + 3$
b. $-3x^7 + 12x^3 + 3x + 3$
c. $15x^{10} + 11x + 6$
d. $9x^{10} + 4x^2 + 3$

Explanation:

Step1: Distribute the negative sign

We have the expression \(12x^{3}+7x + 3-(3x^{7}+4x)\). When we distribute the negative sign to the terms inside the parentheses, we get \(12x^{3}+7x + 3-3x^{7}-4x\).

Step2: Combine like terms

• For the \(x\) terms: \(7x-4x = 3x\)
• The \(12x^{3}\) and \(- 3x^{7}\) and the constant term \(3\) remain as they are since there are no other like terms.

So, combining like terms, we get \(-3x^{7}+12x^{3}+3x + 3\)

Answer:

B. \(-3x^{7}+12x^{3}+3x + 3\)