(10m2-m-9)÷(2m-3)

Rewrite the division as a fraction.

10m2-m-92m-3

For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=10⋅-9=-90 and whose sum is b=-1.

Factor -1 out of -m.

10m2-(m)-92m-3

Rewrite -1 as 9 plus -10

10m2+(9-10)m-92m-3

Apply the distributive property.

10m2+9m-10m-92m-3

10m2+9m-10m-92m-3

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(10m2+9m)-10m-92m-3

Factor out the greatest common factor (GCF) from each group.

m(10m+9)-(10m+9)2m-3

m(10m+9)-(10m+9)2m-3

Factor the polynomial by factoring out the greatest common factor, 10m+9.

(10m+9)(m-1)2m-3

(10m+9)(m-1)2m-3

Simplify (10m^2-m-9)÷(2m-3)