03Cpolynomialvalues

= Polynomial Values =

Recall that for a polynomial P(x) = x 3 + 4x 2 – 2x + 3

P(2) means substitute 2 into P(x) for every incidence of x

... ... P(2) = (2) 3 + 4(2) 2 – 2(2) + 3

... ... P(2) = 8 + 16 – 4 + 3

... ... P(2) = 23

In the same way P(2a) means substitute 2a into P(x) for every incidence of x

... ... P(2a) = (2a) 3 + 4(2a) 2 – 2(2a) + 3

... ... P(2a) = 8a 3 + 16a 2 – 4a + 3

In the same way P(x + 2) means substitute x + 2 into P(x) for every incidence of x

... ... P(x + 2) = (x + 2) 3 + 4(x + 2) 2 – 2(x + 2) + 3

... ... P(x + 2) = ( x 3 + 3(x 2 )(2) + 3(x)(2 2 ) + 2 3 ) + 4 ( x 2 + 4x + 4 ) – ( 2x + 4 ) + 3

... ... P(x + 2) = ( x 3 + 6x 2 + 12x + 8 ) + ( 4x 2 + 16x + 16 ) – ( 2x + 4 ) + 3

... ... P(x + 2) = x 3 + 10x 2 + 26x + 23

Using Casio Classpad calculator to calculate Polynomial Values

You can define the polynomial using the Define command in the ACTION menu, COMMAND submenu


 * Use P from the ABC tab of the virtual keyboard
 * and // **x** // from the keypad or the variable list on the virtual keyboard.
 * powers can be entered using the ^ key from the keypad or in the 2D tab of the virtual keyboard

... ... Define p(x) = x 3  + 4x 2  – 2x + 3


 * When you press EXE you should see DONE
 * Now you can calculate values by entering

... ... p(2)

... ... p(2a)

... ... p(x + 2)


 * the last entry will appear with the brackets.
 * To simplify, use the expand command in the ACTION menu, TRANSFORMATION submenu
 * Drag the previous answer down and drop it after the expand command
 * make sure you have highlighted the whole thing before dragging

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