To find the factor first try to find two such number whose product is equal to 15x^2 and sum is equal to 8x. Such numbers are 5x and 3x.
Evaluate the factor of the equation.
[tex]\begin{gathered} x^2+8x+15=x^2+5x+3x+15 \\ =x(x+5)+3(x+5) \\ =(x+5)(x+3) \end{gathered}[/tex]The equivalent expression is (x+5)(x+3).
To check the factors are correct multiply the factors then original equation is obtained.
[tex]\begin{gathered} (x+5)(x+3)=x\cdot x+3\cdot x+5\cdot x+5\cdot3 \\ =x^2+3x+5x+15 \\ =x^2+8x+15 \end{gathered}[/tex]So factors are correct.
