Polynomial Word Problems

A farmer is planting two types of crops in his field. The yield of the first crop is represented by the polynomial $$3x^2 + 2x + 1$$ and the yield of the second crop is represented by the polynomial $$2x^2 - x + 4$$ . What is the total yield of the two crops?

A company produces two types of widgets. The profit from the first type of widget is given by the polynomial $$4x^2 + 3x - 5$$ , and the profit from the second type of widget is given by the polynomial $$6x^2 - x + 2$$ . What is the difference in profit when the second type of widget's profit is subtracted from the first type's profit?

A rectangular garden has its length represented by the polynomial $$x + 3$$ and its width represented by the polynomial $$x - 2$$ . What is the area of the garden?

A scientist is mixing two solutions. The concentration of the first solution is represented by the polynomial $$5x^3 - 2x^2 + x$$ , and the concentration of the second solution is represented by the polynomial $$-3x^3 + 4x^2 - 2x + 1$$ . What is the resulting concentration when the two solutions are mixed?

A car travels a distance represented by the polynomial $$2x^2 + 3x + 4$$ on the first day and a distance represented by the polynomial $$x^2 - x + 2$$ on the second day. What is the total distance traveled by the car over the two days?

A factory produces two types of products. The cost of producing the first type is given by the polynomial $$7x^2 + 5x - 3$$ , and the cost of producing the second type is given by the polynomial $$4x^2 - 2x + 1$$ . What is the total cost of producing both types of products?

A landscaper is designing two flower beds. The area of the first flower bed is represented by the polynomial $$3x^2 + 4x + 5$$ , and the area of the second flower bed is represented by the polynomial $$x^2 - 2x + 3$$ . What is the difference in area when the second flower bed's area is subtracted from the first flower bed's area?

A chemist is combining two chemicals. The volume of the first chemical is represented by the polynomial $$6x^2 + 2x - 1$$ , and the volume of the second chemical is represented by the polynomial $$3x^2 - x + 4$$ . What is the resulting volume when the two chemicals are combined?

A rectangle has its length represented by the polynomial $$2x + 5$$ and its width represented by the polynomial $$x - 3$$ . What is the area of the rectangle?

A student is solving two polynomial equations. The solution to the first equation is represented by the polynomial $$4x^3 + 3x^2 - x + 2$$ , and the solution to the second equation is represented by the polynomial $$-2x^3 + x^2 + 3x - 1$$ . What is the sum of the solutions to the two equations?