Question

Find the factors of $x^2+22x+112$ by splitting the middle term.

• A. $(x+16)(x+3)$
• B. $(x+9)(x+8)$
• C. $(x+11)(x+8)$
• D. $(x+14)(x+8)$

Answer 1

The correct option is D

$(x+14)(x+8)$

Consider the constant 112.

We need to find two numbers such that product = 112 and sum= coefficient of middle term =22.

14 and 8 are such numbers.

Write the middle term 22x using 14 and 8 as 22x= 14x+8x

$x^2+22x+112$

= $x^2+14x+8x+112$

= $x(x+14)+8(x+14)$

= $(x+14)(x+8)$