(12×2+11x+2)÷(4x+1)

Rewrite the division as a fraction.

12×2+11x+24x+1

For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=12⋅2=24 and whose sum is b=11.

Factor 11 out of 11x.

12×2+11(x)+24x+1

Rewrite 11 as 3 plus 8

12×2+(3+8)x+24x+1

Apply the distributive property.

12×2+3x+8x+24x+1

12×2+3x+8x+24x+1

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(12×2+3x)+8x+24x+1

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

3x(4x+1)+2(4x+1)4x+1

3x(4x+1)+2(4x+1)4x+1

Factor the polynomial by factoring out the greatest common factor, 4x+1.

(4x+1)(3x+2)4x+1

(4x+1)(3x+2)4x+1

Cancel the common factor.

(4x+1)(3x+2)4x+1

Divide 3x+2 by 1.

3x+2

3x+2

Divide (12x^2+11x+2)÷(4x+1)