(11×2-82x+35)÷(x-7)

Rewrite the division as a fraction.

11×2-82x+35x-7

For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=11⋅35=385 and whose sum is b=-82.

Factor -82 out of -82x.

11×2-82(x)+35x-7

Rewrite -82 as -5 plus -77

11×2+(-5-77)x+35x-7

Apply the distributive property.

11×2-5x-77x+35x-7

11×2-5x-77x+35x-7

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(11×2-5x)-77x+35x-7

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

x(11x-5)-7(11x-5)x-7

x(11x-5)-7(11x-5)x-7

Factor the polynomial by factoring out the greatest common factor, 11x-5.

(11x-5)(x-7)x-7

(11x-5)(x-7)x-7

Cancel the common factor.

(11x-5)(x-7)x-7

Divide 11x-5 by 1.

11x-5

11x-5

Divide (11x^2-82x+35)÷(x-7)