Question

What is the additive inverse of the polynomial? –6x3 + 4x2 – 4x

Answer 1

Additive inverse of –6x3 + 4x2 – 4x = Additive inverse of -18+8-4x

=0-(-18+8-4x)

=0-(-10-4x)

=0+10+4x

=10+4x

Answer 2

Answer: The answer is $6x^3-4x^2+4x.$

Step-by-step explanation: We are all familiar with the algebraic famous words like additive identity 0, multiplicative 1, additive inverse, multiplicative inverse, etc.

An additive inverse of a real number is another real number, which when added to the number gives 0. Similar concept holds in case of polynomials.

Let the given polynomial be

$a=6x^3-4x^2+4x.$

And let $b$ be its additive inverse. The, we must have

$a+b=0\\\\\Rightarrow b= -a\\\\\Rightarrow b= -(-6x^3+4x^2-4x)\\\\\Rightarrow b=6x^3-4x^2+4x.$

Thus, the required additive inverse is  $6x^3-4x^2+4x.$