Question

a factor common to x^2 +7x+10 and x^2-3x-10

Answer 1

[tex] x^{2} +7x+10 [/tex]

(Find two numbers such that they when multiplied gives 10 and when added gives 7)

so,
the numbers are 5 and 2
so the factors are (x+5) (x+2)

similarly,
$x^{2} -3x-10$

(Find two numbers such that they when multiplied gives -10 and when added gives -3)

so,
the numbers are -5 and 2
so the factors are (x-5) (x+2)

Thus the common factors are (x+5)(x-5)

Answer 2

x^2+7x+10 =x^2+5x+2x+10 (as we get 5 & 2 From lcm of 10) =x(x+5)+2(x+5) =(x+5)(x+2) x^2-3x-10 =x^2-5x+2x-10 =x(x-5)+2(x-5) =(x-5)(x+2) so the common factor are (x+2).