Question

Which of the following are the factors of $x^2+14x+49$?

• A. 1
• B. a+1
• C. 2
• D. a+2

Answer 1

The correct option is A

1

The expression $x^2+14x+49$ can be written as,

$=x^2+2\times x\times 7+7^2$...(i)

Comparing (i) with identity $(a+b{)}^2=a^2+2ab+b^2$, we get
$a^2=x^2\Rightarrow a=x$

$b^2=7^2\Rightarrow b=7$
$\Rightarrow$ $x^2+14x+49$=$(x+7{)}^2$
Thus, the factors of $x^2+14x+49$ are $(x+7)$ and $(x+7)$.