$\displaystyle\Large\boldsymbol{} x^4+2x^3-2x^2+2x-3= \\\\\\x^4+2x^2(x-1)+2x-\underbrace{2-1}_{-3}= \\\\\\x^4-1+2x^2(x-1)+2x-2 = \\\\\\(x^2-1)(x^2+1)+2x^2(x-1)+2(x-1) = \\\\\\\underline{(x-1)}(x+1)(x^2+1)+2x^2\underline{(x-1)} +2\underline{(x-1)} =\\\\\\(x-1)((x+1)(x^2+1)+2x^2+2)=\\\\\\(x-1)(x^3+x^2+2x^2+x+2+1)=\\\\\\(x-1)(x^3+3x^2+x+3) =\\\\\\(x-1)( \underline{(x+3)}x^2+\underline{(x+3)})=(x^2+1)\underbrace{(x-1)(x+3)}_{x^2+2x-3}= \\\\\\(x^2+1)(x^2+2x-3) : (x^2+2x-3)=x^2+1$

7 0

3 years ago

The table shows the ratio between the number of books ordered and their cost: Find equivalent ratios when the number of books or

Nana76 [90]

Answer:

The answer is below

Step-by-step explanation:

The table shows the ratio between the number of books ordered and their cost: Number of Books Cost (dollars) 7 21 8 24 9 27 Find equivalent ratios when the number of books ordered is 1, 2, and 3. Write them as ordered pairs in the form (x-coordinate, y-coordinate). Starting from the origin, explain how to plot the three equivalent ratios on a coordinate grid.

Answer: Let the number of books be represented as x and the cost (dollars) be represented as y. From the table the ordered pairs in the form (x, y) can be gotten. (7, 21), (8, 24), (9, 27). To get the relationship between the number of books and the cost, we can use the formula of a straight line.

Using point (7, 21) and (8, 24):

$y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-21=\frac{24-21}{8-7}(x-7)\\ \\y-21=3(x-7)\\\\y=3x-21+21\\\\y=3x$

When the number of books ordered is 1, 2, 3 the following pairs are:

For x = 1. y = 3x = 3(1) = 3

For x = 2 y=3x = 3(2) = 6

For x = 3 y = 3x = 3(3) = 9

The ordered pairs are (1, 3), (2, 6), (3, 9)

The graph is attached

To plot the ordered pairs, the number of books are plotted on the x coordinate and the cost on the y coordinate

8 0

3 years ago