Questions and Answers
What is the factored form of $x^2 + 8x + 7$?
What is the factored form of $x^2 - 11x + 10$?
What is the factored form of $x^2 + x - 90$?
What is the factored form of $x^2 + 4x - 12$?
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What is the factored form of $x^2 - 10x + 9$?
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What is the factored form of $x^2 + 16x + 64$?
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What is the factored form of the polynomial $x^2+2x-24$?
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What is the factored form of $x^2 - 4x + 24$?
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What is the factored form of $x^2 - 13x + 40$?
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What is the factored form of the polynomial $x^2 + 11x + 18$?
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What is the factored form of the polynomial $x^2 - x - 56$?
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What is the factored form of the polynomial $x^2 - 5x + 6$?
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What is the factored form of the polynomial $x^2 - 6x + 8$?
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What is the factored form of the polynomial $x^2 + 6x + 8$?
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What is the factored form of the polynomial $x^2 + 2x - 8$?
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What is the factored form of $2x^2 + 22x + 60$?
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What is the factored form of $2x^2 + 6x - 108$?
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What is the factored form of $x^2 - x - 90$?
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What is the factored form of $x^2 + 11x + 10$?
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What is the factored form of $2x^2 + 2x - 4$?
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What is the factored form of $2x^2 - 2x - 4$?
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What is the factored form of $x^2 - 15x + 50$?
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What is the factored form of $x^2 - 7x + 10$?
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What is the factored form of $x^2 + 3x - 18$?
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What is the factored form of $2x^2 + 22x + 20$?
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What is the factored form of $x^2 + 6x - 7$?
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What is the factored form of $x^2 - 6x - 7$?
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What is the factored form of $x^2 - 8x + 7$?
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What is the factored form of $x^2 + 9x - 10$?
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What is the factored form of $x^2 - 9x - 10$?
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What is the factored form of $2x^2 - 6x - 108$?
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What is the factored form of $x^2 - 9$?
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What is the factored form of $x^2 - 25$?
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What is the factored form of $x^2 - 36$?
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What is the factored form of $2x^2 - 32$?
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What is the factored form of $x^2 - 100$?
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What is the factored form of $x^2 - 1$?
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What is the factored form of $2x^2 - 18$?
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What is the factored form of $x^2 - 4$?
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What is the factored form of $x^2 + 4x + 4$?
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What is the factored form of $x^2 - 4x + 4$?
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What is the factored form of $x^2 + 6x + 9$?
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What is the factored form of $x^2 - 6x + 9$?
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What is the factored form of $x^2 + 8x + 16$?
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What is the factored form of $x^2 - 8x + 16$?
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What is the factored form of $x^2 + 10x + 25$?
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What is the factored form of $x^2 - 10x + 25$?
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Study Notes
Factoring Basics
- Factoring involves rewriting a polynomial as a product of simpler polynomials.
- Quadratic expressions typically take the form ( ax^2 + bx + c ).
Common Factoring Techniques
- Two Binomials: Products like ( (x+a)(x+b) ) can be used to factor expressions.
- Perfect Square: Forms such as ( (x+a)^2 ) indicate ( x^2 + 2ax + a^2 ).
- Difference of Squares: ( (x-a)(x+a) = x^2 - a^2 ).
Examples of Factored Forms
- ( (x+7)(x+1) ) represents ( x^2 + 8x + 7 ).
- ( (x-10)(x-1) ) factors to ( x^2 - 11x + 10 ).
- ( (x-9)(x+10) ) leads to ( x^2 + x - 90 ).
Special Cases
- Not Factorable: ( x^2 - 4x + 24 ) cannot be factored over the integers.
- Double Roots: Forms like ( (x-2)^2 ) represent perfect squares, e.g., ( x^2 - 4x + 4 ).
Specific Factoring Examples
- ( 2(x+5)(x+6) ) represents ( 2x^2 + 22x + 60 ).
- Conjugates: ( (x+3)(x-3) ) expands to ( x^2 - 9 ).
Factoring Quadratics with Leading Coefficient
- When the leading coefficient is greater than 1, such as in ( 2x^2 + 22x + 60 ), multiple terms must be considered.
- For instance, ( 2(x+1)(x-2) ) applies to ( 2x^2 - 2x - 4 ).
Factoring Rational Expressions
- Recognizing standard forms helps in identifying how to simplify or factor rational expressions quickly.
Summary of Quadratic Factor Examples
- ( (x-5)(x-2) ) factors to ( x^2 - 7x + 10 ).
- ( (x+10)(x-1) ) provides ( x^2 + 9x - 10 ).
Perfect Square Trinomials
- Recognizing patterns such as:
- ( (x+5)^2 = x^2 + 10x + 25 )
- ( (x-4)^2 = x^2 - 8x + 16 )
Practice and Application
- Regular practice with various forms reinforces understanding and recognition of factors.
- Exploring non-linear forms and higher-degree polynomials can expand learning.
Additional Notes
- Not every polynomial can be factored in simple integer forms, and identifying these instances is part of mastering algebra.
- Dedicating time to each form solidifies the knowledge necessary for factoring in future coursework.
Studying That Suits You
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Description
Test your skills in factoring polynomials with these flashcards designed for Algebra 1. Each card presents a quadratic expression to factor, helping you reinforce your understanding of the topic. Perfect for students looking to practice and improve their factoring techniques.