polynomial function and synthetic division
TRANSCRIPT
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POLYNOMIAL FUNCTION
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Special kind of algebraic expression where each term is constant, a variable or a product of constants and variable raised to whole number exponents.
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The variable has a negative exponent
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The variable is in the denominator
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The variable is in the radical
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The term 5x2+8x-3 where5 is the leading coefficient5x2 is the leading term-3 is the constant
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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
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Example:Identify if the ff. is a function. If yes, identify its kind, leading coefficient, and the constant
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8x17-7x18+6x4-5x+216ANSWER:
Yes, 18th degree polynomial function, -7, 216
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4x3-3x5
ANSWER:Yes, Quintic Function, -3, 0
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Synthetic Division
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synthetic division is an easy process of dividing polynomials by a binomial with the degree
of 1 and has a 1 as leading coefficient
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example:
we can use synthetic division if 3X^2+20X+3
/ X-2
or 10X^6+3X^4+20X-3 /
X+4
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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 | ___|
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Then write the coefficients of the dividend
2 | 3 20 3 __| _____________________
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Bring the 1st no. down
2 | 3 20 3 __| _____________________
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Multiply it to the no. in the box and add it
2 | 3 20 3 __| +6 _____________________ 3 26
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Do step 5 until you get to the last no.
2 | 3 20 3 __| +6 +52 _____________________ 3 26 55
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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
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EXAMPLES
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2 1 3 -7 -9 6
2 10 6 -6
1 5 3 -3 0
+ 3x - 3
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( 2 + 4 x - 8)
-1 2 0 4 -8
-1 1 -5
2 -1 5 13
Final Answer : - 1 x + 5 -
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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
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( - +
2 6 -6
3 6
2 - 3 4 0
Final answer : 2 -3x+ 4
=
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(
0, -1 1 - 3 11 -3 10
1 -3 10 0 0
Final answer :
0 -1
0 3 0 - 10
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