Question

Written as a simplified polynomial in standard form, what is the result when
(x + 1)2 is subtracted from 7x2 - 4x + 6?

Answer 1

Answer:

The resultant polynomial is: $6x^2-6x+5$

Step-by-step explanation:

We need to subtract $(x+1)^{2}$ from $7x^2-4x+6$

so, we start by performing the multiplication involved in the perfect square of the binomial $(x+1)$, and obtain its expression in separate terms that can be combined:

$(x+1)^{2}=(x+1)\,(x+1)=x^2+x+x+1=x^2+2x+1$

Now we can subtract this trinomial from  $7x^2-4x+6$, and  combining like terms to get the resultant polynomial expression:

$7x^2-4x+6-(x^2+2x+1)=7x^2-4x+6-x^2-2x-1=7x^2-x^2-4x-2x+6-1=6x^2-6x+5$

Then the resultant polynomial is: $6x^2-6x+5$