Question

What is the expression in factored form?

-x^2 + 3x + 28

a. (x-7)(x-4)
b. -(x-7)(x+4)
c. (x+4)(x+7)
d. -(x-4)(x+7)

Answer 1

Choice b is correct answer.

Explanation:

Given expression is:

-x²+3x+28

We have to represent above expression in factored form.

Split the middle term of given expression so that the product of two terms should be -28 and their sum be 3.

-x²+7x-4x+28

make two groups and taking common,we get

-x(x-7)-4(x-7)

taking (x-7) as common,we get

(x-7)(-x-4)

As we observed that -1 is common in last term of above expression.

take negative sign as common

-(x-7)(x+4) which is the answer we required.

Answer 2

`\boxed{b.\:\:-(x-7)(x+4)}`

Explanation:

The given expression is
`-x^2+3x+28`

We split the middle term to obtain;

`-x^2+7x-4x+28`

We factor to get;

`-x(x-7)-4(x-7)`

We factor further to obtain;

`=(x-7)(-x-4)`

We factor the negative 1 to get;

`=-(x-7)(x+4)`