The Factor Theorem (Leaving Cert Mathematics): Flashcards

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The Factor Theorem
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What does the Factor Theorem link?

Factors and roots of polynomials

Quadratic equation degree

2

Cubic equation degree

3

Roots in degree 2 polynomial

Two roots

Roots in degree 3 polynomial

Three roots

If P(c)=0P(c)=0, then what is a factor?

(x−c)(x-c)

Factor form of root x=−3x=-3

(x+3)(x+3)

How does a factor divide into polynomial?

Evenly

Test if x=cx=c is root by checking

P(c)=0P(c)=0

Remainder when factor divides evenly

0

Roots shown graphically by

Times equation crosses xx-axis

Quotient used to find

Remaining roots

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Polynomials

The Factor Theorem

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Polynomials

The Factor Theorem

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Polynomials

The Factor Theorem

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Polynomials

The Factor Theorem

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