Given the area of a triangle is 14x^2 +15x+4 and the base is 4x+2,write the algebraic expression for the height

By definition, the area of the triangle is given by:
 A = (1/2) * (b) * (h)
 Where,
 b: base.
 h: height.
 Clearing the height we have:
 h = (2 * A) / (b)
 Substituting:
 h = (2 * (14x ^ 2 + 15x + 4)) / ((4x + 2))
 h = (14x ^ 2 + 15x + 4) / (2x + 1)
 Making the division of polynomials we have:
 h = 7x + 4
 
 the algebraic expression for the height is:
 h = 7x + 4