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5-1: Polynomial Function NOTES Date:
OBJ: Classifying Polynomials
Standard form of polynomials
The goes first. Then write in order. 4x3 + 3x2 + 5x +1
Degree – The largest of the polynomial.
Number of terms
Write each polynomial in standard form. Classify by degree and number of terms.
3x + 9x2 + 5 5x + x + 3 4x + x + 2
3n3 + 1 2n + 5n4 4 1 + 2x2 2 + 3x3 4x
a3(a2 + a + 1) x(x + 5) 5(x + 5)
Example 2: Determine the end behavior of the graph.
Exponent is even
Exponent is odd
**Look at the term with the highest exponent
Determine the end behavior of the polynomial.
Degree = 4 Degree = 2 Degree = 3
Turning points – the number of places the graph switches from to or to . Possible turning points is one less than turning points = n – 1
Write in standard form, determine the end behavior, and find the number of possible turning points
12x4 – x + 3x7 – 1 –x + x2 + 2 50 – 3x3 + 5x2 20 – 5x6 + 3x – 11x3