Question

Consider this expression.

Answer 1

Answer:

Step-by-step explanation:

Hello, first we can develop (x+a)(x+b)

$(x+a)(x+b)=x(x+b)+a(x+b)=x^2+bx+ax+ab=x^2+(a+b)x+ab$

We know that this should be equal to

$x^2+x-72$

So, we can identify the coefficients of the like terms

1 = 1 (terms in $x^2)$

1 =  a + b (terms in x)

-72 = ab (constant term)

72 is 8 * 9 so, -72=9*(-8)

and we have 9 - 8 =1

so, a = 9 and b = -8

$\Large \boxed{\sf \bf \ x^2+x-72=(x+9)(x-8) \ }$

Thank you