Final answer:
To find the expression for the height of the triangle when the area and base are given, substitute the values into the area formula and solve for the height using synthetic division.
Step-by-step explanation:
To find the expression for the height of the triangle, we can rearrange the formula for the area of a triangle and solve for the height. The formula for the area is A = ½(base)(height). We have the area (3x^4 + x^3 - 7x^2 + x - 10) and the base (3x - 5), so we can substitute them into the formula and solve for the height as follows:
A = ½(base)(height)
(3x^4 + x^3 - 7x^2 + x - 10) = ½((3x - 5)(height))
To isolate the height, we need to divide both sides of the equation by ½(3x - 5). To do this, we can use synthetic division. Synthetic division will give us the expression for the height:
Using synthetic division, we divide (3x^4 + x^3 - 7x^2 + x - 10) by (3x - 5) to find the expression for the height.