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)

Algebra I 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

Use the structure of an expression to identify ways to rewrite it.  For example, see x⁴–y⁴ as (x²)²–(y²)², thus recognizing it as a difference of squares that can be factored as (x²–y²)(x²+y²).

AI

AII

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AII