{"id":31583,"date":"2025-06-22T04:24:40","date_gmt":"2025-06-22T04:24:40","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=31583"},"modified":"2025-06-22T04:24:42","modified_gmt":"2025-06-22T04:24:42","slug":"which-expression-is-the-factorization-of-x2-10x-21","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/which-expression-is-the-factorization-of-x2-10x-21\/","title":{"rendered":"Which expression is the factorization of x^2 + 10x + 21"},"content":{"rendered":"\n<p>Which expression is the factorization of x^2 + 10x + 21? O(x + 3)(x + 7) (x + 4)(x + 6) \u00e2\u2014\u2039 (x + 6)(x + 15) O (x + 7)(x + 14)<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The correct factorization of the expression <strong>x\u00b2 + 10x + 21<\/strong> is:<br><strong>\u2714 (x + 3)(x + 7)<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>To factor a quadratic expression of the form <strong>x\u00b2 + bx + c<\/strong>, we look for two numbers that:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Multiply to give the constant term c<\/strong>, which is <strong>21<\/strong><\/li>\n\n\n\n<li><strong>Add to give the middle coefficient b<\/strong>, which is <strong>10<\/strong><\/li>\n<\/ol>\n\n\n\n<p>Let&#8217;s identify all the factor pairs of <strong>21<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>1 and 21 \u2192 1 + 21 = 22<\/li>\n\n\n\n<li>3 and 7 \u2192 3 + 7 = <strong>10<\/strong><\/li>\n\n\n\n<li>Other combinations like -3 and -7 also multiply to 21, but their sum is -10<\/li>\n<\/ul>\n\n\n\n<p>So, the pair <strong>3 and 7<\/strong> works because:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>3 \u00d7 7 = 21<\/strong> (gives the constant)<\/li>\n\n\n\n<li><strong>3 + 7 = 10<\/strong> (gives the middle term)<\/li>\n<\/ul>\n\n\n\n<p>This means we can write the expression as:<\/p>\n\n\n\n<p><strong>x\u00b2 + 10x + 21 = (x + 3)(x + 7)<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Why the other choices are incorrect:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>(x + 4)(x + 6):<\/strong><br>4 \u00d7 6 = 24, and 4 + 6 = 10 \u2192 sum matches but product is <strong>24<\/strong>, not 21<\/li>\n\n\n\n<li><strong>(x + 6)(x + 15):<\/strong><br>6 \u00d7 15 = 90, and 6 + 15 = 21 \u2192 product is wrong, too big<\/li>\n\n\n\n<li><strong>(x + 7)(x + 14):<\/strong><br>7 \u00d7 14 = 98, and 7 + 14 = 21 \u2192 sum matches the constant, not the middle term<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p><strong>(x + 3)(x + 7)<\/strong> is the correct factorization of <strong>x\u00b2 + 10x + 21<\/strong>.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-179.jpeg\" alt=\"\" class=\"wp-image-31584\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-179.jpeg 1024w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-179-300x300.jpeg 300w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-179-150x150.jpeg 150w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-179-768x768.jpeg 768w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Which expression is the factorization of x^2 + 10x + 21? O(x + 3)(x + 7) (x + 4)(x + 6) \u00e2\u2014\u2039 (x + 6)(x + 15) O (x + 7)(x + 14) The Correct Answer and Explanation is: The correct factorization of the expression x\u00b2 + 10x + 21 is:\u2714 (x + 3)(x + [&hellip;]<\/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-31583","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/31583","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=31583"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/31583\/revisions"}],"predecessor-version":[{"id":31585,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/31583\/revisions\/31585"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=31583"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=31583"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=31583"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}