What is the maximum number of terms a fourth-degree polynomial function in standard form can have?

1 answer:

3 0

A polynomial of four terms is sometimes called a quadrinomial, but there's really no need for such words.
Likewise, what is a 4th degree polynomial? Fourth degree polynomials are also known as quartic polynomials. Quartics have these characteristics: Zero to four roots. One, two or three extrema. Zero, one or two inflection points.
The degree of a polynomial is the highest of the degrees of the polynomial's monomials (individual terms) with non-zero coefficients. The degree of a term is the sum of the exponents of the variables that appear in it, and thus is a non-negative integer.
Zero Polynomial. The constant polynomial. whose coefficients are all equal to 0. The corresponding polynomial function is the constant function with value 0, also called the zero map. The zero polynomial is the additive identity of the additive group of polynomials.

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Daniel is printing out copies of a presentation. It takes 3 minutes to print a color copy and 1 minute to print a black-and-whit

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Work the information to set inequalities that represent each condition or restriction.

2) Name the variables.

c: number of color copies
b: number of black-and-white copies

3) Model each restriction:

i) It takes 3 minutes to print a color copy and 1 minute to print a black-and-white copy.

3c + b


ii) He needs to print at least 6 copies ⇒ c + b ≥ 6


iv) And must have the copies completed in no more than 12 minutes ⇒

3c + b ≤ 12


4) Additional restrictions are c ≥ 0, and b ≥ 0 (i.e. only positive values for the number of each kind of copies are acceptable)

5) This is how you graph that:

i) 3c + b ≤ 12: draw the line 3c + b = 12 and shade the region up and to the right of the line.

ii) c + b ≥ 6: draw the line c + b = 6 and shade the region down and to the left of the line.

iii) since c ≥ 0 and b ≥ 0, the region is in the first quadrant.

iv) The final region is the intersection of the above mentioned shaded regions.

v) You can see such graph in the attached figure.