Factor Theorem (Grade 12 NSC Matric Mathematics): Flashcards

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Factor Theorem
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If p(a)=0p(a) = 0, what is (x−a)(x-a) to p(x)p(x)?

A factor of p(x)p(x)

To test if (x−a)(x-a) is a factor, what do you substitute?

x=ax = a into p(x)p(x); if result is 0, it's a factor

If (x+a)(x+a) is a factor, substitute which value?

x=−ax = -a

If remainder R(x)=0R(x) = 0 after polynomial division

The divisor is a factor

First step to factorise a cubic polynomial

Find one linear factor by trial and error

After finding one linear factor of a cubic

Divide to get quadratic, then factorise it

How to verify your factorisation is correct

Expand back to check you get the original polynomial

To confirm (x−k)(x-k) is a factor using Factor Theorem

Show that p(k)=0p(k) = 0

If p(dc)=0p\left(\frac{d}{c}\right) = 0, what is (cx−d)(cx-d)?

A factor of p(x)p(x)

What does Factor Theorem help determine?

Whether one polynomial is a factor of another

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