Unit 5 · Core unit
Rewriting a sum as a product. Factoring is the tool that turns an equation into a set of zeros, which is why it dominates the next unit.
What a strong answer looks like
A strong answer factors completely, including the common factor, before reading anything from the result.
Know
Distribution multiplies every term by every term. The difference of squares and perfect square patterns are worth recognising on sight.
Apply
Expand systematically, then check by substituting a convenient value.
Watch out
Assuming a squared binomial expands to the sum of squares, omitting the middle term.
Study move
Expand a squared binomial and verify at one value of the variable.
Know
Extracting the common factor first makes every subsequent step smaller and often reveals a recognisable pattern.
Apply
Always look for a common factor before any other technique.
Watch out
Skipping the common factor and then failing to factor what remains.
Study move
Factor an expression whose pattern is only visible after the common factor is removed.
Know
A quadratic factors into two binomials whose product reproduces it. The factored form displays the zeros directly.
Apply
Find factors of the constant summing to the linear coefficient, adjusting for a leading coefficient.
Watch out
Stopping when one factor is found rather than factoring completely.
Study move
Factor three quadratics, one with a leading coefficient other than one.
Modeling drill
Factor an area expression completely and state what each factor represents as a dimension.
