# Study sets matching "zeros of polynomials"

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

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

h(x) = (x-1)(3x-2)

k(x) = (x²-4)(x+8)

Polynomial function with zeros at 2 and -3/2

Polynomial function with zeros at -3 and 1/2

Polynomial function with zeros at 1 and 2/3

Polynomial function with zeros at ±2 and -8

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

Polynomial function with zeros at 2 and -3/2

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

Polynomial function with zeros at -3 and 1/2

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…

Remainder Theorem

Possible Zeros

Descartes Rule of Signs

Upper Bound

If dividing by x-a, then the remainder= f(a)

P/Q: factors of the constant/factors of the leading coefficient

-# of positive zeros=the # of sign changes OR an even # less t…

The numbers found after synthetically dividing are all positiv…

Remainder Theorem

If dividing by x-a, then the remainder= f(a)

Possible Zeros

P/Q: factors of the constant/factors of the leading coefficient

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 = 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

1 and -1 theorem

Fundamental theorem of algebra

rational zero test

Descartes rule of signs

sum of polynomials add up to 0

degree of polynomial = total number of zeros

p/q

PNIT

1 and -1 theorem

sum of polynomials add up to 0

Fundamental theorem of algebra

degree of polynomial = total number of zeros

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) =…

-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 = 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 ?

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)

-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 ?