# Study sets matching "zeros of polynomials"

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if the value of the discriminant = 0

if the value of the discriminant is gre…

if the value of the discriminant is gre…

if the value of the discriminant is les…

the roots: real, rational, equal... the parabola is tangent to th…

the roots: real, rational, unequal... the parabola passes twice t…

the roots: real, irrational, unequal, conjugates... the parabola…

the roots: imaginary, conjugates... never touches the x-axis

if the value of the discriminant = 0

the roots: real, rational, equal... the parabola is tangent to th…

if the value of the discriminant is gre…

the roots: real, rational, unequal... the parabola passes twice t…

What is the lead coefficient of... y = 3x…

What is the degree of ... f(x)=x⁴ + 2x³ ?

What is the degree of... y= (x+1)(x-4)(x+…

What is the degree of ... y = (x+5)²(x-8)⁹…

-7

4

3

11

What is the lead coefficient of... y = 3x…

-7

What is the degree of ... f(x)=x⁴ + 2x³ ?

4

Remainder Theorem

Factor Theorem

Rational Roots Theorem

Proving Upper/Lower Bound

insert x into the f(x) function and the result is the remainde…

Plug x into f(x) and if the remainder is 0, then the (x+__) is…

p/q

alternating = lower bound... nonnegative = upper bound

Remainder Theorem

insert x into the f(x) function and the result is the remainde…

Factor Theorem

Plug x into f(x) and if the remainder is 0, then the (x+__) is…

factored form

Standard form

Line of symmetry

Vertex

Algebraic Expression written as the product of the factors.

Ax + By=C, where A, B, and C are not decimals or fractions, wh…

a line that divides a figure into two halves that are mirror i…

A point where two or more straight lines meet.

factored form

Algebraic Expression written as the product of the factors.

Standard form

Ax + By=C, where A, B, and C are not decimals or fractions, wh…

Dividend

Divisor

Quotient

Long Division

A number to be divided by another number

A number by which another number is to be divided

The result of a division problem

Works every time

Dividend

A number to be divided by another number

Divisor

A number by which another number is to be divided

-7

4

3

11

What is the lead coefficient of... y = - 7x⁴ + 4x³-3x+5 ?

What is the degree of ... f(x)=x⁴ + 2x³ ?

What is the degree of... y= (x+1)(x-4)(x+7) ?

What is the degree of ... y = (x+5)²(x-8)⁹ ?

-7

What is the lead coefficient of... y = - 7x⁴ + 4x³-3x+5 ?

4

What is the degree of ... f(x)=x⁴ + 2x³ ?

-7

4

3

11

What is the lead coefficient of... y = - 7x⁴ + 4x³-3x+5 ?

What is the degree of ... f(x)=x⁴ + 2x³ ?

What is the degree of... y= (x+1)(x-4)(x+7) ?

What is the degree of ... y = (x+5)²(x-8)⁹ ?

-7

What is the lead coefficient of... y = - 7x⁴ + 4x³-3x+5 ?

4

What is the degree of ... f(x)=x⁴ + 2x³ ?

-7

4

3

11

What is the lead coefficient of... y = 3x + 5 - 7x⁴ + 4x³ ?

What is the degree of ... f(x)=x⁴ + 2x³ ?

What is the degree of... y= (x+1)(x-4)(x+7) ?

What is the degree of ... y = (x+5)²(x-8)⁹ ?

-7

What is the lead coefficient of... y = 3x + 5 - 7x⁴ + 4x³ ?

4

What is the degree of ... f(x)=x⁴ + 2x³ ?

-7

4

3

11

What is the lead coefficient of... y = - 7x⁴ + 4x³-3x+5 ?

What is the degree of ... f(x)=x⁴ + 2x³ ?

What is the degree of... y= (x+1)(x-4)(x+7) ?

What is the degree of ... y = (x+5)²(x-8)⁹ ?

-7

What is the lead coefficient of... y = - 7x⁴ + 4x³-3x+5 ?

4

What is the degree of ... f(x)=x⁴ + 2x³ ?

-7

4

3

11

What is the lead coefficient of... y = 3x + 5 - 7x⁴ + 4x³ ?

What is the degree of ... f(x)=x⁴ + 2x³ ?

What is the degree of... y= (x+1)(x-4)(x+7) ?

What is the degree of ... y = (x+5)²(x-8)⁹ ?

-7

What is the lead coefficient of... y = 3x + 5 - 7x⁴ + 4x³ ?

4

What is the degree of ... f(x)=x⁴ + 2x³ ?

f(x) = (x+1)²(x-3)⁵

f(x) = (x-1)²(x+2)³

f(x) = (x+1)³(x+6)⁴

f(x) = (x-3)²

Bounces off @ -1... Crosses @ 3

Bounces off @ 1... Crosses @ -2

Crosses @ -1... Bounces off @ -6

Bounces off @ 3

f(x) = (x+1)²(x-3)⁵

Bounces off @ -1... Crosses @ 3

f(x) = (x-1)²(x+2)³

Bounces off @ 1... Crosses @ -2

3 real zeros

4 real zeros

3 real zeros (one double zero)

one real zero

Sketch the graph and identify the number of real zeros:... f(x) =…

Sketch the graph and identify the number of real zeros:... f(x) =…

Sketch the graph and identify the number of real zeros:... y = x³…

Sketch the graph and identify the number of real zeros:... f(x) =…

3 real zeros

Sketch the graph and identify the number of real zeros:... f(x) =…

4 real zeros

Sketch the graph and identify the number of real zeros:... f(x) =…

f(x) = (x - 2)(2x + 3)(x + 1)

g(x) = x(x - 7)

f(x) = x(3x - 1)(x + 4)

4

Polynomial function with zeros at 2, -1, and -3/2

polynomial function with zeros at 0 and 7

polynomial function with zeros at 0, 1/3, and -4

A polynomial of degree 4 has this many x-intercepts

f(x) = (x - 2)(2x + 3)(x + 1)

Polynomial function with zeros at 2, -1, and -3/2

g(x) = x(x - 7)

polynomial function with zeros at 0 and 7

1/2, 5

−5/2, 3, 4

0, 1/2, 1, −1

0, 1 mult. 2

Find the zeros of f(x) = (2x − 1)(x − 5)

Find the zeros of f(x) = (2x + 5)(x^2 − 7x + 12)

Find the zeros of f(x) = x(2x − 1)(x − 1)(x + 1)

Find the zeros of f(x) = x^3 − 2x^2 + x

1/2, 5

Find the zeros of f(x) = (2x − 1)(x − 5)

−5/2, 3, 4

Find the zeros of f(x) = (2x + 5)(x^2 − 7x + 12)

.5, 5

−2.5, 3, 4

0, .5, 1, −1

0, 1

Find the zeros of f(x) = 2x² - 11x + 5

Find the zeros of f(x) = 2x³ - 9x² - 11x + 60

Find the zeros of f(x) = 2x⁴ - x³ - 2x² + x

Find the zeros of f(x) = x³ - 2x² +x

.5, 5

Find the zeros of f(x) = 2x² - 11x + 5

−2.5, 3, 4

Find the zeros of f(x) = 2x³ - 9x² - 11x + 60

Explain the "Affenkasten".

What can multiple zeros of a polynomial…

What is a zeros's "multiplicity"?

What if many graphs have the same zeros?

All cubed polynomials have a point of inflection (Wendepunkt)…

You can find how many times the graph is going to touch or cro…

It refers to the number of times its associated factor appears…

They can still look very different depending on what exponents…

Explain the "Affenkasten".

All cubed polynomials have a point of inflection (Wendepunkt)…

What can multiple zeros of a polynomial…

You can find how many times the graph is going to touch or cro…

1/2, 5

−5/2, 3, 4

1/2, 1, −1

0, 1, 1

Find the zeros of f(x) = (2x − 1)(x − 5)

Find the zeros of f(x) = (2x + 5)(x² − 7x + 12)

Find the zeros of f(x) = 2x³ − x² − 2x + 1

Find the zeros of f(x) = x³ − 2x² + x

1/2, 5

Find the zeros of f(x) = (2x − 1)(x − 5)

−5/2, 3, 4

Find the zeros of f(x) = (2x + 5)(x² − 7x + 12)

f(x)=(x+2)(x-2i)(x+2i)

f(x)=(x+2)^2(x+i)(x-i)

f(x)=(x+2)(x-5+i)(x-5-i)

f(x)=(x+2)(x-i)(x+i)(x+5+i)(x+5-i)

Degree of 3 and zeros -2 and 2i

Degree of 4 and zeros -2 with multiplicity of 2 and -i

Degree of 3 and zeros -2 and 5-i

Degree of 5 and zeros -2, i, and -5-i

f(x)=(x+2)(x-2i)(x+2i)

Degree of 3 and zeros -2 and 2i

f(x)=(x+2)^2(x+i)(x-i)

Degree of 4 and zeros -2 with multiplicity of 2 and -i

Write the polynomial in factored form.

What are the zeros of the function? Gra…

What are the zeros of the function? Wha…

what is the relative maximum and minimu…

4x(x-4)(x+6)

0,-2,-5

The number 0 is a zero multiplicity 2; the numbers 1 and 3 are…

The relative maximum is at (-1.53, 12.01) and the relative min…

Write the polynomial in factored form.

4x(x-4)(x+6)

What are the zeros of the function? Gra…

0,-2,-5