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Stage 4 - Stage 5

Consider the expression $x^3-64$`x`3−64.

a

Factorise this expression.

b

Does $x^3-64$`x`3−64 have any other real-valued linear factors?

Yes

A

No

B

c

State the number of real-valued linear factors that $x^3-64$`x`3−64 has.

Easy

Approx 3 minutes

The polynomial $x^3+5x^2+2x-8$`x`3+5`x`2+2`x`−8 has a factor of $x-1$`x`−1.

Consider the cubic $x^3+4x^2-11x-30$`x`3+4`x`2−11`x`−30.

By looking for linear factors of $12x+x^2-x^3$12`x`+`x`2−`x`3, factorise it completely.

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