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Polynomials of Higher Degree (VCE SSCE Mathematical Methods): Flashcards

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Polynomials of Higher Degree

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Degree of a quartic function

Constraint on $a$ in quartic $f(x) = ax^4 + bx^3 + cx^2 + dx + e$

$a \neq 0$

Max x-intercepts for degree $n$ polynomial

At most $n$

Possible number of x-intercepts for quartic function

0, 1, 2, 3, or 4

Can even degree polynomials have no x-intercepts?

Yes

Min x-intercepts for odd degree polynomial

At least one

Factor theorem: If $P(a) = 0$ , then...

$(x-a)$ is a factor of $P(x)$

Graph behaviour at repeated factor with even power

Touches x-axis but doesn't cross

End behaviour of quartic with $a > 0$

Both ends go to positive infinity

End behaviour of quartic with $a < 0$

Both ends go to negative infinity

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Polynomials of Higher Degree (VCE SSCE Mathematical Methods): Flashcards

Practise the cards

Degree of a quartic function

Constraint on aaa in quartic f(x)=ax4+bx3+cx2+dx+ef(x) = ax^4 + bx^3 + cx^2 + dx + ef(x)=ax4+bx3+cx2+dx+e

Max x-intercepts for degree nnn polynomial

Possible number of x-intercepts for quartic function

Can even degree polynomials have no x-intercepts?

Min x-intercepts for odd degree polynomial

Factor theorem: If P(a)=0P(a) = 0P(a)=0, then...

Graph behaviour at repeated factor with even power

End behaviour of quartic with a>0a > 0a>0

End behaviour of quartic with a<0a < 0a<0

Explore VCE SSCE Mathematical Methods Revision Notes by Topics

Solving Cubic Equations

Cubic Functions of a Particular Form

Graphs of Factorised Cubic Functions

Solving Cubic Inequalities

Families of Cubic Polynomial Functions

Applications of Polynomial Functions

The Bisection Method

Quadratic Functions

Determining the Rule for a Parabola

The Language of Polynomials

Division and Factorisation of Polynomials

The General Cubic Function

Polynomials of Higher Degree

Determining the Rule for the Graph of a Polynomial

Solution of Literal Equations and Systems of Equations

Determining the Rule for a Parabola

The Language of Polynomials

Division and Factorisation of Polynomials

The General Cubic Function

Polynomials of Higher Degree

Determining the Rule for the Graph of a Polynomial

Solution of Literal Equations and Systems of Equations

Explore VCE SSCE Mathematical Methods Model Answers by Topics

Solving Cubic Equations

Cubic Functions of a Particular Form

Graphs of Factorised Cubic Functions

Solving Cubic Inequalities

Families of Cubic Polynomial Functions

Applications of Polynomial Functions

The Bisection Method

Quadratic Functions

Determining the Rule for a Parabola

The Language of Polynomials

Division and Factorisation of Polynomials

The General Cubic Function

Polynomials of Higher Degree

Determining the Rule for the Graph of a Polynomial

Solution of Literal Equations and Systems of Equations

Determining the Rule for a Parabola

The Language of Polynomials

Division and Factorisation of Polynomials

The General Cubic Function

Polynomials of Higher Degree

Determining the Rule for the Graph of a Polynomial

Solution of Literal Equations and Systems of Equations

Explore VCE SSCE Mathematical Methods Quizzes by Topics

Solving Cubic Equations

Cubic Functions of a Particular Form

Graphs of Factorised Cubic Functions

Solving Cubic Inequalities

Families of Cubic Polynomial Functions

Applications of Polynomial Functions

The Bisection Method

Quadratic Functions

Determining the Rule for a Parabola

The Language of Polynomials

Division and Factorisation of Polynomials

The General Cubic Function

Polynomials of Higher Degree

Determining the Rule for the Graph of a Polynomial

Solution of Literal Equations and Systems of Equations

Determining the Rule for a Parabola

The Language of Polynomials

Division and Factorisation of Polynomials

The General Cubic Function

Polynomials of Higher Degree

Determining the Rule for the Graph of a Polynomial

Constraint on $a$ in quartic $f(x) = ax^4 + bx^3 + cx^2 + dx + e$

Max x-intercepts for degree $n$ polynomial

Factor theorem: If $P(a) = 0$ , then...

End behaviour of quartic with $a > 0$

End behaviour of quartic with $a < 0$