The game shown at the right consists of eight pairs of coloured squares called dominos.
Rules:
1. Write a polynomial in each square marked P and a rational function in each square marked R.
2. The expressions you write must satisfy each of these conditions:
• Polynomials and numerators and denominators of each rational function must be quadratics without a constant common factor.
• Restrictions on the variable of each rational function must be stated in its square.
• When two polynomials are side by side, then one or both of the polynomials must be perfect squares.
• When a polynomial and a different-coloured rational expression are side by side, their product must simplify.
• When two rational expressions are side by side, their product must simplify.
• When a polynomial is on top of another polynomial, their quotient must simplify.
• When a polynomial is on top of a different-coloured rational expression (or vice versa), their quotient must simplify.
• When a rational expression is on top of a rational expression, their quotient must simplify.
hi, its naz angain. to see the picture of the work, please type: the words in the bracket
(After you have completed the table, simplify the products and quotients wherever possible. You get one point for every different linear factor that remains in your table.)
please please and please i need to submit this work before the end of tomorrow. thanks
To solve this problem, you need to follow the rules given and satisfy each of the conditions for the expressions you write on each square.
Here is the step-by-step process on how to complete the game:
1. Start with the square marked P1. Since it is the first square, you have more flexibility in choosing the polynomial expression. Make sure it is a quadratic without a constant common factor. For example, you could write P1(x) = x^2.
2. Move to the next square marked R1. Here, you need to write a rational function. Similar to the polynomials, the numerator and denominator of the rational function must be quadratics without a constant common factor. Additionally, you need to state the restrictions on the variable in the square itself. For example, you could write R1(x) = (x^2 + 1)/(x^2 - 1), and state in the square that x ≠ ±1.
3. Continue this process for each square, alternating between polynomials and rational functions, while following the given rules and conditions. Remember to simplify products and quotients as required.
4. When you encounter squares with two adjacent expressions (polynomial and rational, or two rational functions), you need to make sure their product simplifies. For example, if you have P2(x) and R2(x) adjacent, their product should simplify to a quadratic without a constant common factor.
5. Similarly, when you have a polynomial on top of another polynomial, or a polynomial on top of a rational function (or vice versa), their quotient must simplify. For example, if you have P3(x) on top of P4(x), their quotient should simplify to a rational function without a constant common factor.
6. Continue this pattern until you have completed all eight pairs of squares.
Remember to carefully follow the rules and conditions stated for each expression, and make sure to simplify products and quotients accordingly.