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Questions and Answers
Which method is most suitable for factoring the polynomial $2x^3 - 2x^2 - x + 1$?
Which method is most suitable for factoring the polynomial $2x^3 - 2x^2 - x + 1$?
- Perfect square trinomial
- Sum of cubes
- Difference of squares
- Grouping (correct)
What is the fully factored form of the polynomial $36x^2 - 4$?
What is the fully factored form of the polynomial $36x^2 - 4$?
- $4(3x - 1)(3x + 1)$
- Cannot be factored
- $(6x + 2)(6x - 2)$ (correct)
- $(6x - 2)(6x - 2)$
The factored form of $x^2 + 5x - 66$ is $(x - 6)$ times $(x +$ ______ $).
The factored form of $x^2 + 5x - 66$ is $(x - 6)$ times $(x +$ ______ $).
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Describe the initial step required to factor the expression $7x^2 + 35x + 28$ completely.
Describe the initial step required to factor the expression $7x^2 + 35x + 28$ completely.
To solve the chair arrangement problem, where the number of rows is 2 less than the number of chairs per row in a room of 63 chairs, the equation representing this scenario is $x(x-2) = 63$, where x represents the number of chairs per row.
To solve the chair arrangement problem, where the number of rows is 2 less than the number of chairs per row in a room of 63 chairs, the equation representing this scenario is $x(x-2) = 63$, where x represents the number of chairs per row.
Flashcards
What is factoring a polynomial?
What is factoring a polynomial?
Separating a polynomial into simpler polynomials such that when multiplied together, they give the original polynomial.
What is the first step in factoring?
What is the first step in factoring?
Check for common factors in all terms, then look for special patterns (difference of squares, perfect square trinomials), or use techniques like grouping or trial and error.
What is the difference of squares?
What is the difference of squares?
A polynomial in the form a^2 - b^2 factors into (a + b)(a - b).
How to determine if a quadratic is factorable?
How to determine if a quadratic is factorable?
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How to solve word problems involving factoring?
How to solve word problems involving factoring?
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Study Notes
- Factoring polynomials involves selecting the appropriate method and ensuring complete factorization.
Factoring Polynomials
- To factorize $x^3 - 2x^2 - 9x + 18$, consider factoring by grouping
- To factorize $8x^3 - 64$, consider the difference of cubes
- To factorize $8x^2 - 8x - 6$, consider factoring a trinomial/quadratic
- To factorize $36x^2 - 49$, consider difference of squares
- To factorize $x^2 + 5x - 66$, consider factoring a trinomial/quadratic
- To factorize $x^2 - 10x - 48$, consider factoring a trinomial/quadratic
- To factorize $9x^3 + 27x^2$, consider factoring out the greatest common factor
- To factorize $7x^2 + 35x + 28$, consider factoring out the greatest common factor and then factoring the resulting trinomial
- To factorize $3x^3 - 12x^2 - 9x + 36$, consider factoring by grouping
- To factorize $16x^2 - 8x + 1$, consider factoring a perfect square trinomial
- To factorize $1 - 4x^2$, consider difference of squares
- To factorize $3x^2 - 11x + 10$, consider factoring a trinomial/quadratic
Problem Solving with Equations
- A room with 63 chairs has the number of rows being 2 less than the number of chairs per row; to find the number of chairs per row, set up an equation where $x(x-2) = 63$
- To solve number problems where one number is 2 larger than another, and the sum of their squares is 100, set up an equation where $x^2 + (x+2)^2 = 100$ and solve for $x$
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Description
Learn how to factor polynomials by grouping, difference of cubes, trinomial/quadratic, difference of squares, greatest common factor, and perfect square trinomial. Master polynomial factorization techniques. This guide helps you choose the appropriate method and ensure complete factorization.
