Question

When asked to factor the trinomial x^2-14x+49, a student gives the answer (x-7)(x+7). which of the following statements is true?

A. The answer is incorrect; the plus sign should be a minus sign.
B. The answer is incorrect; The minus sign should be a plus sign.
C. The answer is incorrect; the 7's should be 14's.
D. The answer is correct.

Answer 1

Your answer is A: The answer is incorrect; the plus sign should be a minus sign.

The verified answer's formatting was a bit confusing.

Answer 2

Option A. The answer is incorrect; the plus sign should be a minus sign

Explanation:

we have

`x^(2)-14x+49`

we know that

`(x-b)^(2)=x^(2)-2bx+b^(2)`

Solve for b

`-2bx=-14x\\2b=14\\b=7`

`b^(2)=49\\b=7`

therefore

`x^(2)-14x+49=(x-7)^2=(x-7)(x-7)`

Verify each case

case A) The answer is incorrect; the plus sign should be a minus sign

The statement is true

case B) The answer is incorrect; The minus sign should be a plus sign

The statement is false

Because, the plus sign should be a minus sign

case C) The answer is incorrect; the 7's should be 14's

The statement is false

case D) The answer is correct

The statement is false