Core Algebra 2 concepts: polynomial factoring, rational expressions, and exponential and logarithmic functions, explained conceptually.
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- What does it mean to factor a polynomial completely?
- Write it as a product of polynomials that cannot be factored further (over the reals or rationals, depending on context).
- State the difference of squares factoring pattern.
- a^2 - b^2 = (a + b)(a - b)
- What is the greatest common factor (GCF) of a polynomial?
- The largest expression that divides evenly into every term of the polynomial.
- Describe the factoring technique called factoring by grouping.
- Group terms into pairs, factor out the GCF from each pair, then factor out the common binomial from the resulting expression.
- State the sum of cubes factoring pattern.
- a^3 + b^3 = (a + b)(a^2 - ab + b^2)
- State the difference of cubes factoring pattern.
- a^3 - b^3 = (a - b)(a^2 + ab + b^2)
- Explain the zero product property.
- If a product equals zero, then at least one factor must equal zero.
- When you factor out a common binomial from an expression, what does that binomial do?
- It becomes one factor in the final factored form.
- Describe the general strategy for factoring a trinomial ax^2 + bx + c.
- Find two numbers that multiply to ac and add to b, use them to split the middle term, then factor by grouping.
- What is a rational expression?
- A fraction where the numerator and denominator are both polynomials.
- What values must be excluded from the domain of a rational expression?
- Any values that make the denominator equal to zero.
- How do you simplify a rational expression?
- Factor the numerator and denominator, then cancel common factors.
- To add or subtract rational expressions with different denominators, what is the first step?
- Find the least common denominator (LCD) and rewrite each fraction with that denominator.
- How do you multiply two rational expressions?
- Multiply the numerators together and multiply the denominators together, then simplify if possible.
- How do you divide two rational expressions?
- Multiply the first expression by the reciprocal of the second, then simplify.