Question

What is the constant term in the polynomial expression -7x2 + 32x + 240, and what does it represent?

What's the factored form of that expression and what do the factors represent?

Answer 1

Given:

The polynomial expression
`-7x^2+32x+240`.

To find:

The constant term in the polynomial expression and factored form.

Solution:

We have

`-7x^2+32x+240`

Here, 240 is free from variable x. So, it is the constant term.

It represents the initial value of the expression, where x=0.

Using splitting the middle term, we get

`-7x^2-28x+60x+240`

`\Rightarrow -7x(x+4)+60(x+4)`

`\Rightarrow  (x+4)(-7x+60)`

Therefore, the factored form is
`(x+4)(-7x+60)`.

It represents the two expressions, whose product is the given expression.