{"id":4447,"date":"2016-10-03T21:18:17","date_gmt":"2016-10-03T21:18:17","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/?post_type=chapter&p=4447"},"modified":"2017-07-27T17:10:43","modified_gmt":"2017-07-27T17:10:43","slug":"introduction-10","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-suffolkccc-intermediatealgebra\/chapter\/introduction-10\/","title":{"raw":"Why It Matters: Factoring","rendered":"Why It Matters: Factoring"},"content":{"raw":"

Why learn how to factor?<\/h3>\r\nThere are hard ways to do things and there are easy ways to do things. For example, you can free climb the brick wall of your apartment building\u00a0and crawl into the third floor window. Or you could take the stairs. Easier still, you could use the elevator. Math also offers efficient ways to accomplish a task.\r\n\r\nRemember Joan? Joan has a friend, Nate, who is never far from his phone or a computer. \u00a0Nate posts numerous pictures, videos, memes, quips, and links on his various social media accounts daily. \u00a0Joan follows Nate on Instagram and has lately been annoyed with the sheer number of his posts. She wants to let him know that he is probably annoying others, too, but she doesn't want to hurt his feelings.\r\n\r\nSince Joan is studying polynomial functions in her math class, she comes up with a plan. \u00a0She will appeal to Nate's data-savvy, technical side by proposing that you can fall out of favor with your Instagram followers by posting too many times in one day.\r\n\r\nShe sees\u00a0the following polynomial function in her math homework:\r\n\r\n[latex]L(x)=-x^2+4x[\/latex]\r\n\r\n\"Instagram\"\r\n\r\nIn this function, Joan decides that x represents the number of pictures posted on Instagram each day by her friend Nate. L(x), then, represents the number of likes or comments his\u00a0pictures on Instagram receive based on the number posted. If he doesn't post any, obviously no one will like his pictures.\r\n\r\nIf Nate posts too many, people will get bored of his\u00a0spam and ignore him. Joan\u00a0wants to know how much is too much so Nate\u00a0can stay popular on Instagram, and not become an annoying spammer. By solving this polynomial function for zero, Joan hopes to find out exactly how many is too many posts for Nate. This translates to, when will he get zero likes or comments on his Instagram pictures?\r\n\r\n\"Ho\r\n\r\nJoan is not sure how to solve this kind of equation, so she\u00a0starts guessing values for x.\r\n\r\nHer first guess is 10, since Nate posts more than that.\r\n\r\n[latex]L(10)=-10^2+4(10)=-100+40=-60[\/latex]\r\n\r\nWhoa, if Nate posts 10 pictures on Instagram each day, he will get -60 likes or comments. Joan\u00a0assumes negative numbers aren't a good thing.\r\n\r\nNext, she guesses 5.\r\n\r\n[latex]L(5)=-5^2+4(5)=-25+20=-5[\/latex]\r\n\r\nOK, Joan is\u00a0getting closer.\r\n\r\nThen Joan\u00a0asks herself, why am I guessing the solution to a math problem when I can ask my math teacher how to solve it?\r\n\r\nThe point is that there are hard ways to do things, and there are easier ways to do things. The hard way to solve a quadratic equation such as [latex]0 =-x^2+4x[\/latex] is to guess. An easier way is to factor.","rendered":"

Why learn how to factor?<\/h3>\n

There are hard ways to do things and there are easy ways to do things. For example, you can free climb the brick wall of your apartment building\u00a0and crawl into the third floor window. Or you could take the stairs. Easier still, you could use the elevator. Math also offers efficient ways to accomplish a task.<\/p>\n

Remember Joan? Joan has a friend, Nate, who is never far from his phone or a computer. \u00a0Nate posts numerous pictures, videos, memes, quips, and links on his various social media accounts daily. \u00a0Joan follows Nate on Instagram and has lately been annoyed with the sheer number of his posts. She wants to let him know that he is probably annoying others, too, but she doesn’t want to hurt his feelings.<\/p>\n

Since Joan is studying polynomial functions in her math class, she comes up with a plan. \u00a0She will appeal to Nate’s data-savvy, technical side by proposing that you can fall out of favor with your Instagram followers by posting too many times in one day.<\/p>\n

She sees\u00a0the following polynomial function in her math homework:<\/p>\n

[latex]L(x)=-x^2+4x[\/latex]<\/p>\n

\"Instagram\"<\/p>\n

In this function, Joan decides that x represents the number of pictures posted on Instagram each day by her friend Nate. L(x), then, represents the number of likes or comments his\u00a0pictures on Instagram receive based on the number posted. If he doesn’t post any, obviously no one will like his pictures.<\/p>\n

If Nate posts too many, people will get bored of his\u00a0spam and ignore him. Joan\u00a0wants to know how much is too much so Nate\u00a0can stay popular on Instagram, and not become an annoying spammer. By solving this polynomial function for zero, Joan hopes to find out exactly how many is too many posts for Nate. This translates to, when will he get zero likes or comments on his Instagram pictures?<\/p>\n

\"Ho<\/p>\n

Joan is not sure how to solve this kind of equation, so she\u00a0starts guessing values for x.<\/p>\n

Her first guess is 10, since Nate posts more than that.<\/p>\n

[latex]L(10)=-10^2+4(10)=-100+40=-60[\/latex]<\/p>\n

Whoa, if Nate posts 10 pictures on Instagram each day, he will get -60 likes or comments. Joan\u00a0assumes negative numbers aren’t a good thing.<\/p>\n

Next, she guesses 5.<\/p>\n

[latex]L(5)=-5^2+4(5)=-25+20=-5[\/latex]<\/p>\n

OK, Joan is\u00a0getting closer.<\/p>\n

Then Joan\u00a0asks herself, why am I guessing the solution to a math problem when I can ask my math teacher how to solve it?<\/p>\n

The point is that there are hard ways to do things, and there are easier ways to do things. The hard way to solve a quadratic equation such as [latex]0 =-x^2+4x[\/latex] is to guess. An easier way is to factor.<\/p>\n","protected":false},"author":21,"menu_order":1,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-4447","chapter","type-chapter","status-publish","hentry"],"part":146,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/suny-suffolkccc-intermediatealgebra\/wp-json\/pressbooks\/v2\/chapters\/4447","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/suny-suffolkccc-intermediatealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/suny-suffolkccc-intermediatealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-suffolkccc-intermediatealgebra\/wp-json\/wp\/v2\/users\/21"}],"version-history":[{"count":2,"href":"https:\/\/courses.lumenlearning.com\/suny-suffolkccc-intermediatealgebra\/wp-json\/pressbooks\/v2\/chapters\/4447\/revisions"}],"predecessor-version":[{"id":4551,"href":"https:\/\/courses.lumenlearning.com\/suny-suffolkccc-intermediatealgebra\/wp-json\/pressbooks\/v2\/chapters\/4447\/revisions\/4551"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/suny-suffolkccc-intermediatealgebra\/wp-json\/pressbooks\/v2\/parts\/146"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/suny-suffolkccc-intermediatealgebra\/wp-json\/pressbooks\/v2\/chapters\/4447\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/suny-suffolkccc-intermediatealgebra\/wp-json\/wp\/v2\/media?parent=4447"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-suffolkccc-intermediatealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=4447"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-suffolkccc-intermediatealgebra\/wp-json\/wp\/v2\/contributor?post=4447"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-suffolkccc-intermediatealgebra\/wp-json\/wp\/v2\/license?post=4447"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}