11/11/2023 0 Comments Illuminate math lesson![]() There is nothing wrong with writing a polynomial equation like \(y=6x^2+5x^3+4x\), but the largest exponent in a polynomial can tell you a lot about the polynomial, so it’s recommended to start with that term. Lastly, tell students that polynomials are typically written so that the term with the highest exponent is first. If no students bring it up as a strategy for thinking about the equation, display the graphs of \(y=5x^3+6x^2+4x\) and \(y=5640\) on the same axes using a window where the intersection of the two graphs is visible, and ask students about the meaning of the point of intersection \((10,5640)\). Select 2–3 students to explain their thinking about the last question. ![]() The benefits and drawbacks of each form will be discussed in more depth in future lessons. This form, that is, fully expanded with no parentheses, is often called standard form, while the equation for the volume of the box was written in factored form. Begin the discussion by telling students that while \(p(x)\) may look different than the equation for the volume of a box, it is still a polynomial. There are even cases where we would want to divide polynomials, which students will look at in future lessons. In fact, polynomials act a lot like the number system in that we can add, subtract, and multiply polynomials to get other polynomials. The goal of this discussion is to make sure students understand that polynomials can represent decimal forms of numbers.
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