Question

Express the sum of the polymonial 3x^2+15x-56 and the square of the binomial (x-8) as a polynomial in standard form.

Answer 1

Given:

Polynomial is
`3x^2+15x-56`.

To find:

The sum of given polynomial and the square of the binomial (x-8) as a polynomial in standard form.

Solution:

The sum of given polynomial and the square of the binomial (x-8) is

`3x^2+15x-56+(x-8)^2`

`=3x^2+15x-56+x^2-2(x)(8)+8^2`
`[\because (a-b)^2=a^2-2ab+b^2]`

`=3x^2+15x-56+x^2-16x+64`

On combining like terms, we get

`=(3x^2+x^2)+(15x-16x)+(-56+64)`

`=4x^2-x+8`

Therefore, the sum of given polynomial and the square of the binomial (x-8) as a polynomial in standard form is
`4x^2-x+8`.