Polynomials Degree Writing Equations

Write a polynomial function of least degree with integral coefficients that has the given zeros.

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What is a leading coefficient?

• The coefficient that is non-existent.

• The coefficient of the term with the lowest degree.

• The coefficient of the term with the highest degree.

What method is being used in the image?

• FIND

• FIOL

• FOIL

• FIRE

What is a Monomial?

• Polynomial consisting of 3 terms.

• Polynomial consisting of one term.

• 3xy³

• 3yz+5yz⁵

What is a Polynomial?

• 3x(5x+8)

• Dividend of 5 or more terms.

• A type of shape

• Sum of one or more Monomials.

What is the standard form for a Polynomial?

• Degrees must drop from left to right. Like terms must be combined.

• Degrees drop from right to left. Like terms do not have to be combined.

• 3x⁸+ 4x⁵

• 3x²+3x³

How do you add polynomials vertically?

• Line up like terms vertically.

  Fill in the spaces where there are no like terms.

  Add like a normal addition problem

• 2+2

• Combine terms subtract.

• It is impossible to add polynomials.

How to multiply a monomial by a polynomial?

• Remove all variables in the polynomial then multiply.

• Combining like terms

• A single term polynomial.

• Distribute the monomial throughout the polynomial.

Select the polynomial whose zeros and degree are given by: Zeros: – 5(multiplicity of 3), 9(multiplicity of 2), – 2, 4 Degree: 7

• (x + 5)³(x - 9)²(x + 2)(x - 4)

• (x + 5)³(x - 9)²(x + 2)⁷(x - 4)⁷

• (x + 5)³(x - 9)²(x + 2)

• (x + 5)(x - 9)(x + 2)(x - 4)

The degree and the sign of the leading coefficient (positive or negative) of a polynomial determines the behavior of the ends for the graph. Determine the end behavior of this equation. f(x) = -x⁵ - 4x +2

• As x goes to negative infinity, y goes to positive infinity. As x goes to positive infinity, y goes to positive infinity.

• As x goes to negative infinity, y goes to positive infinity. As x goes to positive infinity, y goes to negative infinity.

• As x goes to negative infinity, y goes to negative infinity. As x goes to positive infinity, y goes to positive infinity.

• As x goes to negative infinity, y goes to negative infinity. As x goes to positive infinity, y goes to negative infinity.