Writing Polynomial Functions from Zeros

This video tutorial explains polynomial functions, focusing on understanding zeros and their role in forming polynomial equations. It covers converting zeros into factors, transforming polynomials from factored to standard form, and using distribution and box methods for multiplication. The tutorial concludes with sketching polynomial graphs, emphasizing the importance of zeros and multiplicity.

What is another name for the zeros of a polynomial function?

• Extremes

• Intercepts

• Vertices

• Roots

If a polynomial has a zero at x = 3, how can it be written as a factor?

• x / 3

• x * 3

• x - 3

• x + 3

What does it mean if a zero is repeated in a polynomial function?

• It is a double root

• It is a complex root

• It is an imaginary root

• It is a simple root

How do you convert a polynomial from factored form to standard form?

• By adding the factors

• By multiplying the factors

• By dividing the factors

• By subtracting the factors

What is the first step in multiplying two binomials?

• Adding the coefficients

• Subtracting the constants

• Distributing each term

• Combining like terms

What is the result of multiplying (x - 3)(x - 3)?

• x^2 - 6x + 9

• x^2 + 6x + 9

• x^2 - 9

• x^2 + 9

What method can be used to multiply a trinomial by a binomial?

• Lattice method

• Cross method

• Box method

• FOIL method

How do you identify a polynomial in standard form?

• The exponents are in ascending order

• The coefficients are all negative

• The coefficients are all positive

• The exponents are in descending order

What does a multiplicity of 2 indicate about a zero?

• The zero is imaginary

• The graph touches the x-axis at that zero

• The graph crosses the x-axis at that zero

• The zero is complex

What is the shape of the graph of a cubic polynomial with a positive leading coefficient?

• It forms a parabola

• Both ends go up

• Both ends go down

• One end goes up and the other goes down