Podcast
Questions and Answers
What is the definition of the expression $x^2 - 4$?
What is the definition of the expression $x^2 - 4$?
- perfect square
- difference of squares (correct)
- binomial product
- sum of squares
What is the factorization of $x^2 + 2x - 8$?
What is the factorization of $x^2 + 2x - 8$?
factor directly
What is the factorization of $v^2n - 2v^2 - 4n + 8$?
What is the factorization of $v^2n - 2v^2 - 4n + 8$?
(n-2)(v^2-4)
What are the two numbers that multiply to -30 and add to 13?
What are the two numbers that multiply to -30 and add to 13?
What method is used in the problem $4x^2 - 25$?
What method is used in the problem $4x^2 - 25$?
What is the factorization of $x^2 + 12x + 35$?
What is the factorization of $x^2 + 12x + 35$?
What is the factorization of the trinomial $3x^2 + 7x - 20$ using MARFF?
What is the factorization of the trinomial $3x^2 + 7x - 20$ using MARFF?
What is the factorization of $6a^3 - 3a^2 + 8a - 4$ by grouping?
What is the factorization of $6a^3 - 3a^2 + 8a - 4$ by grouping?
What is the factorization of $4p^6 - 49$ using the difference of squares method?
What is the factorization of $4p^6 - 49$ using the difference of squares method?
Is the expression $x^2 + 23x + 11$ factorable?
Is the expression $x^2 + 23x + 11$ factorable?
What is the factorization of $4x^2 - 25$?
What is the factorization of $4x^2 - 25$?
What is the factorization of $x^2 + 16x - 105$?
What is the factorization of $x^2 + 16x - 105$?
What is the factorization of $4x^3 + 28x^2 - 3x - 21$?
What is the factorization of $4x^3 + 28x^2 - 3x - 21$?
What is the simplified form of the polynomial $(3x + 7) + (3x + 7) + (2x - 3) + (2x - 3)$?
What is the simplified form of the polynomial $(3x + 7) + (3x + 7) + (2x - 3) + (2x - 3)$?
What is the area of a rectangle with sides $(2x - 3)$ and $(3x + 7)$?
What is the area of a rectangle with sides $(2x - 3)$ and $(3x + 7)$?
Flashcards
Difference of Squares
Difference of Squares
An expression representing the difference between two squared terms.
Factorization
Factorization
Finding the factors that multiply together to give the original expression.
Numbers that Multiply/Add
Numbers that Multiply/Add
Two numbers whose product equals one number and sum equals another.
MARFF Method
MARFF Method
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Factorization by Grouping
Factorization by Grouping
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Factor the trinomial x^2 + 12x + 35
Factor the trinomial x^2 + 12x + 35
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Simplifying a Polynomial
Simplifying a Polynomial
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Area of a Rectangle
Area of a Rectangle
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Study Notes
Factoring Types and Techniques
- Difference of Squares: Expresses as (a^2 - b^2 = (a - b)(a + b)). Example: (x^2 - 4) factors to ((x - 2)(x + 2)).
- Trinomial Factoring: Directly factor polynomials of the form (x^2 + bx + c). Example: (x^2 + 12x + 35) factors to ((x + 7)(x + 5)).
- Grouping Method: Used for polynomials with four terms, grouping pairs for factoring. Example: (6a^3 - 3a^2 + 8a - 4) factors to ((2a - 1)(3a^2 + 4)).
Solving Polynomials
- Factoring Trinomials: Combine two numbers that multiply to (c) and add to (b). Example: For (x^2 + 2x - 8), factors into ((x + 4)(x - 2)).
- Polynomials with Multiple Methods: Different methods may suit various expressions. Example: (4x^2 - 25) can be solved using the difference of squares to give ((2x - 5)(2x + 5)).
Number Properties
- Numbers that multiply to give a negative product and add up to a positive can include one positive and one negative. Example: The numbers for -30 that add to 13 are 15 and -2.
Factorability
- Some polynomials cannot be factored using integers. Example: (x^2 + 23x + 11) is not factorable with rational coefficients.
- Completely factorable forms include products of simpler binomials or trinomial expressions. Example: (x^2 + 16x - 105) factors into ((x + 21)(x - 5)).
Polynomial Simplification
- Simplicity is key for polynomial expressions. Example: Adding ((3x + 7)) twice and ((2x - 3)) twice simplifies to (10x + 8).
- When finding areas of geometric shapes, expand product forms. Example: The area of a rectangle with sides ((2x - 3)) and ((3x + 7)) simplifies to (6x^2 + 5x - 21).
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