POLYNOMIAL FUNCTION

Special kind of algebraic expression where each term is constant, a variable or a product of constants and variable raised to whole number exponents.

The variable has a negative exponent

The variable is in the denominator

The variable is in the radical

The term 5x2+8x-3 where5 is the leading coefficient5x2 is the leading term-3 is the constant

A function is defined by p(x) = anxn+an-xn-1+…a1x+ab where n is a positive integer. An-1; An-2 are called polynomial functions

Example:Identify if the ff. is a function. If yes, identify its kind, leading coefficient, and the constant

8x17-7x18+6x4-5x+216ANSWER:

Yes, 18th degree polynomial function, -7, 216

4x3-3x5

ANSWER:Yes, Quintic Function, -3, 0

Synthetic Division

synthetic division is an easy process of dividing polynomials by a binomial with the degree

of 1 and has a 1 as leading coefficient

example:

we can use synthetic division if 3X^2+20X+3

/ X-2

or 10X^6+3X^4+20X-3 /

X+4

Steps: Let's take (3X^2+20X+3)/ (X-2)

Then write the coefficients of the dividend

2 | 3 20 3 ___|

_____________________ the sign of the constant in the divisor and

put it in the box 2 | ___|

Then write the coefficients of the dividend

2 | 3 20 3 __| _____________________

Bring the 1st no. down

2 | 3 20 3 __| _____________________

Multiply it to the no. in the box and add it

2 | 3 20 3 __| +6 _____________________ 3 26

Do step 5 until you get to the last no.

2 | 3 20 3 __| +6 +52 _____________________ 3 26 55

Then get the degree of the divisor and subtract 1

2-1 = 1

The degree of the quotient is 1

so .. 3X+26.. .then the last no. 55 is the remainder

EXAMPLES

2 1 3 -7 -9 6

2 10 6 -6

1 5 3 -3 0

+ 3x - 3

( 2 + 4 x - 8)

-1 2 0 4 -8

-1 1 -5

2 -1 5 13

Final Answer : - 1 x + 5 -

Find the remainder when the polynomial -2x -4 is divided by x-3 using synthetic division

3 3 -2 4 9 21

3 7 17

The remainder is 17

( - +

2 6 -6

3 6

2 - 3 4 0

Final answer : 2 -3x+ 4

=

(

0, -1 1 - 3 11 -3 10

1 -3 10 0 0

Final answer :

0 -1

0 3 0 - 10

Members:

Blancas, LaidezIglesia, MijsCardillo, Jay LeiPacheco, Dara JeanetteRivera, Harriet