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POLYNOMIAL
FUNCTION
The term 5x2+8x-3 where
5 is the leading coefficient
5x2 is the leading term
-3 is the constant
Example:
Identify if the ff. is a function. If
yes, identify its kind, leading
coefficient, and the constant
8x17-7x18+6x4-5x+216
ANSWER:
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
(𝑥4
+3𝑥3
− 7𝑥2
+ 13 𝑥 − 5 ) ÷ (𝑥 − 2)
2 1 3 -7 -9 6
2 10 6 -6
1 5 3 -3 0
𝐹𝑖𝑛𝑎𝑙 𝐴𝑛𝑠𝑤𝑒𝑟 ∶ 𝑥3 +5 𝑥2 + 3x - 3
( 2 𝑥3
+ 4 x - 8) ÷ (𝑥 + 1 )
-1 2 0 4 -8
-1 1 -5
2 -1 5 13
Final Answer : 2 𝑥2 - 1 x + 5 -
13
𝑥+1
Find the remainder when the polynomial 𝑥2 -2x -4
is divided by x-3 using synthetic division
3 3 -2 4
9 21
3 7 17
The remainder is 17
( 4 𝑥3 - 12 𝑥2 + 17 𝑥 − 12 ) ÷ (2𝑥 − 3 )
𝟑
𝟐 2 6
17
2
-6
3
9
2
6
2 - 3 4 0
Final answer : 2 𝑥2
-3x+ 4
4 𝑥3 − 12 𝑥2 + 17 𝑥 −12
2𝑥 −3
=
4𝑥3 −12 𝑥2 17 𝑥 −12 ÷2
2𝑥−3 ÷2
=
2𝑥3 −6 𝑥2+
17
2
𝑥 −6
𝑥−
3
2
(𝑥4
− 3𝑥3
+ 11 𝑥2
− 3x + 10) ÷ (𝑥2
+ 1 )
0, -1 1 - 3 11 -3 10
1 -3 10 0 0
Final answer : 𝑥2 − 3𝑥 + 10
0 -1
0 3
0 - 10
Members:
Blancas, Laidez
Iglesia, Mijs
Cardillo, Jay Lei
Pacheco, Dara Jeanette
Rivera, Harriet

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Polynomial Function and Synthetic Division