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

Answer:

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

Step-by-step 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

Answer 2

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.