{"id":32687,"date":"2025-06-22T17:42:50","date_gmt":"2025-06-22T17:42:50","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=32687"},"modified":"2025-06-22T17:42:51","modified_gmt":"2025-06-22T17:42:51","slug":"practice-your-skill","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/practice-your-skill\/","title":{"rendered":"Practice Your Skill"},"content":{"rendered":"\n

Practice Your Skill: Factor completely- 1 62 + 8b + 7 2 n^2 + 1ln + 10 3 n^2 – 10n + 9 4. n^2 + 4n – 12 5. m^2 + m – 9 6. m^2 + Zm – 24 7. x^2 – 4x + 24 8 k^2 – 13k + 40 9. a^2 + 1la + 18 10. n^2 – n – 56<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Here are the completely factored forms of the given expressions:<\/p>\n\n\n\n

    \n
  1. b2+8b+7=(b+1)(b+7)b^2 + 8b + 7 = (b + 1)(b + 7)<\/li>\n\n\n\n
  2. n2\u221211n+10=(n\u22121)(n\u221210)n^2 – 11n + 10 = (n – 1)(n – 10)<\/li>\n\n\n\n
  3. n2\u221210n+9=(n\u22121)(n\u22129)n^2 – 10n + 9 = (n – 1)(n – 9)<\/li>\n\n\n\n
  4. n2+4n\u221212=(n+6)(n\u22122)n^2 + 4n – 12 = (n + 6)(n – 2)<\/li>\n\n\n\n
  5. m2+m\u221290=(m+10)(m\u22129)m^2 + m – 90 = (m + 10)(m – 9)<\/li>\n\n\n\n
  6. m2+2m\u221224=(m+6)(m\u22124)m^2 + 2m – 24 = (m + 6)(m – 4)<\/li>\n\n\n\n
  7. x2\u22124x+24x^2 – 4x + 24 cannot be factored over the integers<\/li>\n\n\n\n
  8. k2\u221213k+40=(k\u22125)(k\u22128)k^2 – 13k + 40 = (k – 5)(k – 8)<\/li>\n\n\n\n
  9. a2+11a+18=(a+2)(a+9)a^2 + 11a + 18 = (a + 2)(a + 9)<\/li>\n\n\n\n
  10. n2\u2212n\u221256=(n\u22128)(n+7)n^2 – n – 56 = (n – 8)(n + 7)<\/li>\n<\/ol>\n\n\n\n

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

    Factoring quadratic trinomials relies on identifying two binomials whose product yields the original expression. For a general quadratic of the form ax2+bx+cax^2 + bx + c, we look for two numbers that multiply to acac and add to bb. In these problems, all leading coefficients aa are 1, which simplifies the process.<\/p>\n\n\n\n

    Take example 4: n2+4n\u221212n^2 + 4n – 12. We search for two numbers that multiply to -12 and sum to +4. The pair 6 and -2 fits. Thus, we rewrite it as (n+6)(n\u22122)(n + 6)(n – 2).<\/p>\n\n\n\n

    In example 7, x2\u22124x+24x^2 – 4x + 24, no integer pair multiplies to 24 and adds to -4. Since its discriminant (\u22124)2\u22124(1)(24)=16\u221296=\u221280(-4)^2 – 4(1)(24) = 16 – 96 = -80 is negative, it has no real roots and cannot be factored over the integers.<\/p>\n\n\n\n

    This process reinforces algebraic fluency and pattern recognition. Factoring is essential for solving quadratic equations, simplifying expressions, and analyzing polynomial functions. Mastery of it provides a foundation for more advanced topics like completing the square, quadratic formula application, and graphing.<\/p>\n\n\n\n

    \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

    Practice Your Skill: Factor completely- 1 62 + 8b + 7 2 n^2 + 1ln + 10 3 n^2 – 10n + 9 4. n^2 + 4n – 12 5. m^2 + m – 9 6. m^2 + Zm – 24 7. x^2 – 4x + 24 8 k^2 – 13k + 40 9. a^2 […]<\/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-32687","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/32687","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=32687"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/32687\/revisions"}],"predecessor-version":[{"id":32695,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/32687\/revisions\/32695"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=32687"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=32687"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=32687"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}