Math - 2017-18
AII.1d and *AII.1c - Factoring Polynomials
AII.1 The student, given rational, radical, or polynomial expressions, will
d) factor polynomials completely.
AII.1 The student will
c) factor polynomials completely in one or two variables.
Bloom's Level: Evaluate
- I can design the track of a
roller coaster, determine the sloped curve of an exit ramp, trace the free
falling path of a skydiver, and
understand the mechanics of controllers like
autopilot, cruise control, and a living room thermostat.
- I will
apply mathematical processes for basic operations to algebraic expressions and
divide algebraic terms out of algebraic expressions.
UNDERSTANDING THE STANDARD
- Computational skills applicable to numerical
fractions also apply to rational expressions involving variables.
- Radical expressions can be written and
simplified using rational exponents.
- Only radicals with a common radicand and index
can be added or subtracted.
- A relationship exists among arithmetic complex
fractions, algebraic complex fractions, and rational numbers.
- The complete factorization of polynomials has
occurred when each factor is a prime polynomial.
- Pattern recognition can be used to determine
complete factorization of a polynomial.
· The complete factorization of polynomials has occurred when each factor is a prime polynomial.
· Pattern recognition can be used to determine complete factorization of a polynomial.
· Polynomials may be factored in various ways, including, but not limited to grouping or applying general patterns such as difference of squares, sum and difference of cubes, and perfect square trinomials.
Greatest Common Factor
Binomials (squares, cubes)
All.1d1 Factor polynomials by applying general patterns including difference of squares, sum and difference of cubes, and perfect square trinomials.
All.1d2 Factor polynomials completely over the integers.
· AII.1c1 Factor polynomials in one or two variables with no more than four terms completely over the set of integers. Factors of the polynomial should be constant, linear, or quadratic.
All.1d3 Verify polynomial identities: difference of squares, sum and difference of cubes, and perfect square trinomials.
· AII.1c2 Verify polynomial identities including the difference of squares, sum and difference of cubes, and perfect square trinomials.
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