Find the factors of $x^2+9x+20$ and then compare it with $x^2+(a+b)x+ab$.

Given :

Given equation is $x^2+9x+20.$

To do :

We have to factorise it and compare with $x^2+(a+b)x+ab$

Solution :

To factorise it we have to find two numbers whose sum is equal to the coefficient of x and the product is equal to the constant term.

$9x=(4+5)x$    [$4\times5=20$]

Therefore,

 $x^2+9x+20$=$x^2+(4+5)x+4\times5$

Comparing it with $x^2+(a+b)x+ab$, we get,

a=4 and b=5.

$x^2+9x+20$=$x^2+(4+5)x+4\times5$

                         =$x^2+4x+5x+4\times5$

                         =$x(x+4)+5(x+4)$

                         =$(x+4)(x+5)$

The factors of $x^2+9x+20$ are $(x+4)$ and $(x+5)$.

Tutorialspoint

Updated on: 10-Oct-2022

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