{"id":44666,"date":"2025-06-30T18:09:49","date_gmt":"2025-06-30T18:09:49","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=44666"},"modified":"2025-06-30T18:09:53","modified_gmt":"2025-06-30T18:09:53","slug":"which-equation-is-set-up-for-direct-use-of-the-zero-factor-property","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/which-equation-is-set-up-for-direct-use-of-the-zero-factor-property\/","title":{"rendered":"Which equation is set up for direct use of the zero-factor property"},"content":{"rendered":"\n

Which equation is set up for direct use of the zero-factor property? Solve it. <\/p>\n\n\n\n

A. 3 x squared minus 17 x minus 6 equals 0 <\/p>\n\n\n\n

B. left parenthesis 5 x plus 6 right parenthesis squared equals 7 <\/p>\n\n\n\n

C. x squared plus x equals 6 <\/p>\n\n\n\n

D. left parenthesis 3 x minus 1 right parenthesis left parenthesis x minus 4 right parenthesis equals 0<\/p>\n\n\n\n

The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n

The equation that is set up for direct use of the zero-factor property is D<\/strong>: (3x\u22121)(x\u22124)=0(3x – 1)(x – 4) = 0<\/p>\n\n\n\n

Explanation:<\/h3>\n\n\n\n

The Zero-Product Property<\/strong> states that if the product of two expressions equals zero, then at least one of the expressions must be zero. Mathematically, if: (a)(b)=0(a)(b) = 0<\/p>\n\n\n\n

then either a=0a = 0 or b=0b = 0.<\/p>\n\n\n\n

In equation D, the product of (3x\u22121)(3x – 1) and (x\u22124)(x – 4) is set equal to zero. To use the zero-product property, we can set each factor equal to zero individually: 3x\u22121=0orx\u22124=03x – 1 = 0 \\quad \\text{or} \\quad x – 4 = 0<\/p>\n\n\n\n

Solving each equation:<\/h4>\n\n\n\n
    \n
  1. For 3x\u22121=03x – 1 = 0:<\/strong> 3x=13x = 1 x=13x = \\frac{1}{3}<\/li>\n\n\n\n
  2. For x\u22124=0x – 4 = 0:<\/strong> x=4x = 4<\/li>\n<\/ol>\n\n\n\n

    So the solutions to the equation (3x\u22121)(x\u22124)=0(3x – 1)(x – 4) = 0 are x=13x = \\frac{1}{3} and x=4x = 4.<\/p>\n\n\n\n

    Why the other options don\u2019t fit the zero-factor property:<\/h3>\n\n\n\n
      \n
    • Option A<\/strong> (3×2\u221217x\u22126=0)(3x^2 – 17x – 6 = 0): This is a quadratic equation. Although it could potentially be factored, it is not set up as the product of two factors equaling zero, which is necessary for the zero-product property.<\/li>\n\n\n\n
    • Option B<\/strong> (5x+6)2=7(5x + 6)^2 = 7: This equation involves a square, not a product of two terms set equal to zero. It would require other methods, such as isolating xx, to solve.<\/li>\n\n\n\n
    • Option C<\/strong> (x2+x=6)(x^2 + x = 6): This equation would need to be rearranged into a quadratic form (x2+x\u22126=0x^2 + x – 6 = 0) before it could be factored and solved, but it\u2019s not directly in the form for zero-factor property use.<\/li>\n<\/ul>\n\n\n\n

      Hence, the correct choice is D<\/strong>: (3x\u22121)(x\u22124)=0(3x – 1)(x – 4) = 0.<\/p>\n","protected":false},"excerpt":{"rendered":"

      Which equation is set up for direct use of the zero-factor property? Solve it. A. 3 x squared minus 17 x minus 6 equals 0 B. left parenthesis 5 x plus 6 right parenthesis squared equals 7 C. x squared plus x equals 6 D. left parenthesis 3 x minus 1 right parenthesis left parenthesis […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-44666","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/44666","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=44666"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/44666\/revisions"}],"predecessor-version":[{"id":44667,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/44666\/revisions\/44667"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=44666"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=44666"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=44666"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}