Algebra 1 Factoring Practice Flashcards
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Questions and Answers

What is the factored form of $x^2 + 8x + 7$?

  • (x+7)(x+1) (correct)
  • (x-10)(x-1)
  • (x-2)(x+6)
  • (x-9)(x+10)

    • What is the factored form of $x^2 - 11x + 10$?

  • (x-10)(x-1) (correct)
  • (x-3)(x-4)
  • (x+8)(x+8)
  • (x-9)(x+10)

    • What is the factored form of $x^2 + x - 90$?

  • (x-6)(x+15)
  • (x-9)(x+10) (correct)
  • (x+5)(x-18)
  • (x+8)(x-10)

    • What is the factored form of $x^2 + 4x - 12$?

    <p>(x-2)(x+6)</p> Signup and view all the answers

    What is the factored form of $x^2 - 10x + 9$?

    <p>(x-1)(x-9)</p> Signup and view all the answers

    What is the factored form of $x^2 + 16x + 64$?

    <p>(x+8)^2</p> Signup and view all the answers

    What is the factored form of the polynomial $x^2+2x-24$?

    <p>(x+6)(x-4)</p> Signup and view all the answers

    What is the factored form of $x^2 - 4x + 24$?

    <p>Not Factorable</p> Signup and view all the answers

    What is the factored form of $x^2 - 13x + 40$?

    <p>(x-5)(x-8)</p> Signup and view all the answers

    What is the factored form of the polynomial $x^2 + 11x + 18$?

    <p>(x+2)(x+9)</p> Signup and view all the answers

    What is the factored form of the polynomial $x^2 - x - 56$?

    <p>(x+7)(x-8)</p> Signup and view all the answers

    What is the factored form of the polynomial $x^2 - 5x + 6$?

    <p>(x-2)(x-3)</p> Signup and view all the answers

    What is the factored form of the polynomial $x^2 - 6x + 8$?

    <p>(x-4)(x-2)</p> Signup and view all the answers

    What is the factored form of the polynomial $x^2 + 6x + 8$?

    <p>(x+2)(x+4)</p> Signup and view all the answers

    What is the factored form of the polynomial $x^2 + 2x - 8$?

    <p>(x+4)(x-2)</p> Signup and view all the answers

    What is the factored form of $2x^2 + 22x + 60$?

    <p>2(x+5)(x+6)</p> Signup and view all the answers

    What is the factored form of $2x^2 + 6x - 108$?

    <p>2(x+9)(x-6)</p> Signup and view all the answers

    What is the factored form of $x^2 - x - 90$?

    <p>(x-10)(x+9)</p> Signup and view all the answers

    What is the factored form of $x^2 + 11x + 10$?

    <p>(x+10)(x+1)</p> Signup and view all the answers

    What is the factored form of $2x^2 + 2x - 4$?

    <p>2(x-1)(x+2)</p> Signup and view all the answers

    What is the factored form of $2x^2 - 2x - 4$?

    <p>2(x+1)(x-2)</p> Signup and view all the answers

    What is the factored form of $x^2 - 15x + 50$?

    <p>(x-10)(x-5)</p> Signup and view all the answers

    What is the factored form of $x^2 - 7x + 10$?

    <p>(x-5)(x-2)</p> Signup and view all the answers

    What is the factored form of $x^2 + 3x - 18$?

    <p>(x-3)(x+6)</p> Signup and view all the answers

    What is the factored form of $2x^2 + 22x + 20$?

    <p>2(x+10)(x+1)</p> Signup and view all the answers

    What is the factored form of $x^2 + 6x - 7$?

    <p>(x+7)(x-1)</p> Signup and view all the answers

    What is the factored form of $x^2 - 6x - 7$?

    <p>(x-7)(x+1)</p> Signup and view all the answers

    What is the factored form of $x^2 - 8x + 7$?

    <p>(x-7)(x-1)</p> Signup and view all the answers

    What is the factored form of $x^2 + 9x - 10$?

    <p>(x+10)(x-1)</p> Signup and view all the answers

    What is the factored form of $x^2 - 9x - 10$?

    <p>(x-10)(x+1)</p> Signup and view all the answers

    What is the factored form of $2x^2 - 6x - 108$?

    <p>2(x-9)(x+6)</p> Signup and view all the answers

    What is the factored form of $x^2 - 9$?

    <p>(x+3)(x-3)</p> Signup and view all the answers

    What is the factored form of $x^2 - 25$?

    <p>(x-5)(x+5)</p> Signup and view all the answers

    What is the factored form of $x^2 - 36$?

    <p>(x+6)(x-6)</p> Signup and view all the answers

    What is the factored form of $2x^2 - 32$?

    <p>2(x-4)(x+4)</p> Signup and view all the answers

    What is the factored form of $x^2 - 100$?

    <p>(x-10)(x+10)</p> Signup and view all the answers

    What is the factored form of $x^2 - 1$?

    <p>(x+1)(x-1)</p> Signup and view all the answers

    What is the factored form of $2x^2 - 18$?

    <p>2(x+3)(x-3)</p> Signup and view all the answers

    What is the factored form of $x^2 - 4$?

    <p>(x+2)(x-2)</p> Signup and view all the answers

    What is the factored form of $x^2 + 4x + 4$?

    <p>(x+2)^2</p> Signup and view all the answers

    What is the factored form of $x^2 - 4x + 4$?

    <p>(x-2)^2</p> Signup and view all the answers

    What is the factored form of $x^2 + 6x + 9$?

    <p>(x+3)^2</p> Signup and view all the answers

    What is the factored form of $x^2 - 6x + 9$?

    <p>(x-3)^2</p> Signup and view all the answers

    What is the factored form of $x^2 + 8x + 16$?

    <p>(x+4)^2</p> Signup and view all the answers

    What is the factored form of $x^2 - 8x + 16$?

    <p>(x-4)^2</p> Signup and view all the answers

    What is the factored form of $x^2 + 10x + 25$?

    <p>(x+5)^2</p> Signup and view all the answers

    What is the factored form of $x^2 - 10x + 25$?

    <p>(x-5)^2</p> Signup and view all the answers

    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.

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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.

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