Question

Written as a simplified polynomial in standard form, what is the result when (3x+7)^2 is subtracted from 3?

Answer 1

Given:

`(3x+7)^2` is subtracted from 3.

To find:

The result of the given statement in the standard form of the polynomial.

Solution:

We need to find the result when
`(3x+7)^2` is subtracted from 3.

So, the resulted polynomial can be written as:

`P(x)=3-(3x+7)^2`

On simplification, we get

`P(x)=3-((3x)^2+2(3x)(7)+(7)^2)`
`[\because (a+b)^2=a^2+2ab+b^2]`

`P(x)=3-(9x^2+42x+49)`

`P(x)=3-9x^2-42x-49`

`P(x)=-9x^2-42x-46`

Therefore, the resulted polynomial in standard form is
`-9x^2-42x-46`.