STANDARD A.SSE.A.2
AI

Recognize and use the structure of an expression to identify ways to rewrite it.  e.g.,

• x3-x2-x=x(x2-x-1)

• 532-472=(53+47)(53-47)

• 16x2-36=(4x)2-(6)2=(4x+6)(4x-6)=4(2x+3)(2x-3) or
  16x2-36=4(4x2-9)=4(2x+3)(2x-3)

• -2x2+8x+10=-2(x2–4x–5)=-2(x-5)(x+1)

• x4+6x2-7=(x2+7)(x2-1)=(x2+7)(x+1)(x-1)

Expressions are limited to numerical and polynomial expressions in one variable.  Use factoring techniques such as factoring out a greatest common factor, factoring the difference of two perfect squares, factoring trinomials of the form ax2+bx+c with a lead coefficient of 1, or a combination of methods to factor completely. Factoring will not involve factoring by grouping and factoring the sum and difference of cubes.

AII

Recognize and use the structure of an expression to identify ways to rewrite it.  e.g.,

• 81x4-16y4 is equivalent to (9x2)2-(4y2)2 or (9x2-4y2)(9x2+4y2) or (3x+2y)(3x-2y)(9x2+4y2)

• (x2+4)/(x2+3) is equivalent to ((x2+3)+1)/(x2+3)=((x2+3)/(x2+3))+(1/(x2+3))=1+(1/(x2+3))

• 3x3+5x2-48x+80 is equivalent to 3x(x2-16)-5(x2-16), which when factored completely is (3x-5)(x+4)(x-4)

Includes factoring by grouping and factoring the sum and difference of cubes.  Tasks are limited to polynomial, rational, or exponential expressions.  Quadratic expressions include leading coefficients other than 1.  This standard is a fluency expectation.  The ability to see structure in expressions and to use this structure to rewrite expressions is a key skill in everything from advanced factoring (e.g., grouping) to summing series, to rewriting of rational expressions, to examining the end behavior of the corresponding rational function.