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

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

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`