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7.8: Factoring Expressions and Solving by Factoring- Answers to the Homework Exercises

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    GCF and Grouping

    1. \(9+8b^2\)
    1. \(7(8-5p)\)
    1. \(-3a^2b(1-2ab)\)
    1. \(10(2x^4-3x+3)\)
    1. \(5(6b^9+ab-3a^2)\)
    1. \(5x^3y^2z(4x^5z + 3x^2 + 7y)\)
    1. \(5q(6pr-p+1)\)
    1. \(-10x^{11}(4+2x-5x^2+5x^3)\)
    1. \(x-5\)
    1. \(10(5x-8y)\)
    1. \(4x^3(2y^2+1)\)
    1. \(3(7p^6+10p^2+9)\)
    1. \(3(7p^6+10p^2+9)\)
    1. \(3(p+4q-5q^2r^2)\)
    1. \(7b(4+2b+5b^2+b^4)\)
    1. \(-4x^2(6x^4+x^2-3x-1)\)
    1. \((8r^2-5)(5r-1)\)
    1. \((3b^2-7)(5b+7)\)
    1. \((7x^2-4)(5x-4)\)
    1. \((8x+3)(4y+5x)\)
    1. \((2x+7y^2)(y-4x)\)
    1. \((4u+3)(8v-5)\)
    1. \((3u-7)(v-2u)\)
    1. \((5x^2-8)(7x-2)\)
    1. \((6x^2+5)(x-8)\)
    1. \((7n^2-5)(n+3)\)
    1. \((3a+b^2)(5b-2)\)
    1. \((m-5)(5n+2)\)
    1. \(2(u+3)(2v+7u)\)
    1. \((7a-2)(8b-7)\)

    Factoring Trinomials of the Form \(x^2+bx+c\)

    1. \((p+9)(p+8)\)
    1. \((x+1)(x-10)\)
    1. \((x-7)(x+10)\)
    1. \((p+6)(p+9)\)
    1. \((u-5v)(u-3v)\)
    1. \((x-9y)(x-2y)\)
    1. \((x+6y)(x-2y)\)
    1. \(6(a-4)(a+8)\)
    1. \(6(x+9y)(x+7y)\)
    1. \((x-5)(x+6)\)
    1. \((b-10)(b-7)\)
    1. \((a+3)(a-9)\)
    1. \((m-5n)(m-10n)\)
    1. \((x+8y)(x+2y)\)
    1. \((x+5y)(x+9y)\)
    1. \(5(n-8)(n-1)\)
    1. \(5(m^2+6mn-18n^2)\)

    Factoring Trinomials of the Form \(ax^2+bx+c\)

    1. \(p=1\)
    1. \(p=1\)
    1. \((7x-6)(x-6)\)
    1. \((5a+7)(a-4)\)
    1. \((2x+5)(x+7)\)
    1. \((5k+3)(k+2)\)
    1. \((3x+2y)(x+5y)\)
    1. \(3(2x+1)(x-7)\)
    1. \(2(7x-2)(x-4)\)
    1. \((k-4)(4k-1)\)
    1. \((m-3n)(4m+3n)\)
    1. \(2(2x+7y)(3x+5y)\)
    1. \((7n-2)(n-6)\)
    1. Prime, not factorable
    1. \((7x-6)(x+5)\)
    1. \((3r+7)(r+3)\)
    1. \((7x+5y)(x-y)\)
    1. \(2(5a+3)(a-6)\)
    1. \((r+1)(4r-3)\)
    1. \((r-1)(4r+7)\)
    1. \(2(2x^2-3xy+15y^2)\)
    1. \(4(x+3y)(4x+3y)\)
    1. \((x-2y+9)(x-2y-2)\)
    1. \((5a-3b+4)(5a-3b+4)\)
    1. \((w^{1/5}+8)(w^{1/5}-10)\)
    1. \((x^{1/3}+10)(x^{1/3}-2)\)

    Special Products

    1. \((r+4)(r-4)\)
    1. \((p+2)(p-2)\)
    1. \(3(x+3)(x-3)\)
    1. \(2(3a+5b)(3a-5b)\)
    1. \((x+3)^2\)
    1. \((5p-1)^2\)
    1. \((2a-5b)^2\)
    1. \((2-m)(4+2m+m^2)\)
    1. \((6-u)(36+6u+u^2)\)
    1. \((4x+3y)(16x^2-12xy+9y^2)\)
    1. \((a^2+9)(a+3)(a-3)\)
    1. \((x^2+y^2)(x+y)(x-y)\)
    1. \((x+3)(x-3)\)
    1. \((2v+1)(2v-1)\)
    1. \(5(n+2)(n-2)\)
    1. \(4(m^2+16n^2)\)
    1. \((n-4)^2\)
    1. \((x+1)^2\)
    1. \(2(3m-2n)^2\)
    1. \((x+4)(x^2-4x+16)\)
    1. \((5x-6)(25x^2+30x+36)\)
    1. \(4(2m-3n)(4m^2+6mn+9n^2)\)
    1. \((x^2+16)(x+4)(x-4)\)
    1. \((4a^2+b^2)(2a+b)(2a-b)\)

    Factoring, A General Strategy

    1. \(3(2a+5y)(4z-3h)\)
    1. \(-2(x-4y)(x^2+4xy+16y^2)\)
    1. \(2(3u-2)(9u^2+6u+4)\)
    1. \((x-3y)(x-y)\)
    1. \((m+2n)(m-2n)\)
    1. \(2(4+3x)(16-12x+9x^2)\)
    1. \(n(n+2)(n+5)\)
    1. \(x(5x+2)\)
    1. \((m-4x)(n+3)\)
    1. \(3(3m+4n)(3m-4n)\)
    1. \(2(m-2n)(m+5n)\)
    1. \(4(2x+3y)^2\)
    1. \(x(2x+3y)(x+y)\)
    1. \((5x+3)(x-5)\)
    1. \((x-3y)(x^2+3xy+9y^2)\)
    1. \(3m(m+2n)(m-4n)\)
    1. \((3a+x^2)(c+5d^2)\)
    1. \((4a+3b)(4a-3b)\)
    1. \(2(4x+3y)(4x-3y)\)
    1. \(v(v+1)\)
    1. \(3n^2(3n-1)\)

    Solve by Factoring

    1. \(7,-2\)
    1. \(-5,5\)
    1. \(-\dfrac{5}{7},-3\)
    1. \(4,0\)
    1. \(\dfrac{3}{7},-8\)
    1. \(-4,-3\)
    1. \(\dfrac{8}{3},-5\)
    1. \(-4,1\)
    1. \(-\dfrac{5}{2},-8\)
    1. \(-4,3\)
    1. \(4,-8\)
    1. \(-\dfrac{7}{8},8\)
    1. \(8,0\)
    1. \(-\dfrac{1}{7},-8\)
    1. \(8,-4\)
    1. \(-\dfrac{1}{2},\dfrac{5}{3}\)
    1. \(2,-3\)
    1. \(-\dfrac{6}{5},-7\)
    1. \(5,7\)

    Solve Applications by Factoring

    1. \(8,13\)
    1. \(6,8\)
    1. \(4,11\)
    1. \(4,7\)
    1. \(6,9\)
    1. \(13\times 9\) inches
    1. \(9\times 5\) inches
    1. \(10\times 4\) inches
    1. \(12\times 8\) inches
    1. \(11\times 8\) inches
    1. \(7\) seconds
    1. \(16\) units

    This page titled 7.8: Factoring Expressions and Solving by Factoring- Answers to the Homework Exercises is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Darlene Diaz (ASCCC Open Educational Resources Initiative) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.