Question

What would be the first and last terms of the polynomial if it was rewritten in standard form? Answer these quickly without performing all of the indicated operations: (a)- (2x^3 − x^2 − 9x +7) +(11x^2 − 6x^3+ 2x − 9) (b)- (x − 3)(2x +3)(x − 1) (c)- (2x − 3)(3x+ 5) − (x +1)(2x^2 − 6x+ 3)

Answer 1

(a) So first term will be
`-4x^3\ and\ last\ term\ will\ be -2`

(b) So first term will be
`2x^3\ and\ last\ term\ will\ be\ 9`

(c) So first term will be
`-2x^3\ and\ last\ term\ will\ be -12`

Explanation:

We have to find the first and last term of the expression

(a) We have given expression
`(2x^3-x^2-9x+7)+(11x^2-6x^3+2x-9)`

After addition it will be
`-4x^3+10x^2-7x-2`

So first term will be
`-4x^3\ and\ last\ term\ will\ be -2`

(b) We have given equation
`(x-3)(2x+3)(x-1)`

After multiplication it will be

`2x^3-5x^2-12x+9`

So first term will be
`2x^3\ and\ last\ term\ will\ be\ 9`

(c) We have given expression
`(2x-3)(3x+5)-(x+1)(2x^2-6x+3)`

It can be written as
`6x^2+x-15-(2x^3-4x^2-3x-3)`

`6x^2+x-15-(2x^3-4x^2-3x-3)=-2x^3+10x^2+4x-12`

So first term will be
`-2x^3\ and\ last\ term\ will\ be -12`