Question

Find the factors of $x^2+8x+15$ by splitting the middle term.

• A. $(x+7)(x+5)$
• B. $(x+3)(x+5)$
• C. $(x+3)(x+8)$
• D. $(x+9)(x+5)$

Answer 1

The correct option is B

$(x+3)(x+5)$

Consider the constant 15.

We need to find two numbers such that product = 15 and sum= coefficient of middle term =8 .

3 and 5 are such numbers.

Write the middle term 8x using 3 and 5 as 8x= 3x+5x

$x^2+8x+15$

= $x^2+3x+5x+15$

= $x(x+3)+5(x+3)$

= $(x+3)(x+5)$