Question

Find the factors of $x^2+8x+16$ by splitting the middle term.

• A. $(x+3)(x+4)$
• B. $(x+2)(x+4)$
• C. $(x+3)(x+3)$
• D. $(x+4)(x+4)$

Answer 1

Given $x^2+8x+16$
Consider the middle term $8x$:
We need to find two numbers such that product $=16$ and sum $=$ coefficient of middle term $=8$ .
Thus,$4$ and $4$ are such numbers.
Now, write the middle term $8x$
Using $4$ and $4$ as $8x=4x+4x$
Consider $x^2+8x+16$
$=x^2+4x+4x+16$
$=x(x+4)+4(x+4)$
$=(x+4)(x+4)$
Hence, the correct option is (D).