{"id":66960,"date":"2018-06-25T20:41:41","date_gmt":"2018-06-25T20:41:41","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=66960"},"modified":"2018-06-25T20:41:41","modified_gmt":"2018-06-25T20:41:41","slug":"factoring-101","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/factoring-101\/","title":{"rendered":"Factoring 101"},"content":{"rendered":"

Although factoring is a fundamental skill of high school level math, many students experience difficulties. If this includes you, keep reading to become an expert at factoring! \u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

The Golden Rule: Common Factor First<\/b><\/h3>\n

Common factoring is the process of finding numbers and\/or variables that are a multiple of every term in an expression and removing them. For example, 2 and x are both common factors of the expression 2x^3 + 8x^2 + 12x. \u00a0Once these have been identified, we divide them out of the expression and determine what remains. Keeping with the above example, factoring out 2 and x would give 2x(x^2 + 4x + 6). By “pulling out” the common factors, the remaining expression becomes simpler and easier to handle. \u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

The Basic Approach to Quadratics: Decomposition <\/b><\/h3>\n

Quadratics are the most common expression that high school students factor. Decomposition is a relatively simple and <\/span>\u00a0full-proof<\/span> approach to these problems. Just follow these steps:<\/span><\/p>\n

1) Identify the a, b, and c values. For those who need a refresher ax^2 + bx + c is the standard form of a quadratic.<\/strong><\/p>\n

for example, with 4x^2 – 12x + 5<\/p>\n

a = 4, b = -12, c = 5 <\/span><\/p>\n

2) Find two numbers that multiply to the product of ac and add to the value of b. \u00a0\u00a0<\/strong><\/p>\n

for example, <\/span>with \u00a04x^2 – 12x + 5<\/p>\n

the numbers are -2 and -10 since (-2) + (-10) = (-12) and (-2)(-10) = 20<\/span><\/p>\n

3) Rewrite the quadratic with your numbers instead of b (this is the decomposition part). <\/strong><\/p>\n

for example, 4x^2 – 12x + 5 \u00a0\u00a0becomes <\/span><\/p>\n

4x^2 -2x -10x + 5 \u00a0\u00a0or <\/span><\/p>\n

4x^2 -10x -2x + 5<\/span><\/p>\n

4) Common factor the the halves of the expressions separately.<\/strong><\/p>\n

for example, with <\/span>4x^2 -2x<\/span> -10x + 5,\u00a0<\/span>it becomes <\/span><\/p>\n

2x(2x-1)<\/span> -5(2x-1)<\/span><\/p>\n

with <\/span>\u00a04x^2 -10x<\/span> -2x + 5<\/span><\/p>\n

it becomes <\/span>2x(2x-5)<\/span> – (2x-5)<\/span><\/p>\n

5) Common factor step 4’s expression<\/strong><\/p>\n

for exmaple, with \u00a02x(2x-1)-5(2x-1)<\/span><\/p>\n

the answer is (2x-1) (2x-5)<\/span><\/p>\n

with 2x(2x-5) – (2x-5) <\/span><\/p>\n

the answer is (2x-5) (2x-1)<\/span><\/p>\n

Shortcuts:<\/b><\/h3>\n

Luckily some shortcuts exist to make life easier! <\/span><\/p>\n

Simple Trinomials: <\/b><\/p>\n

If the a value is 1, this is called a simple trinomial. \u00a0Using the numbers from step 2), skip to the answer, <\/span>inserting these numbers straight into the brackets with x.<\/span><\/p>\n

for example, with x^2 +3x +2 <\/span><\/p>\n

a = 1<\/span><\/p>\n

the numbers are 1 and 2 since 1+2 = 3 and (1)(2) = 2<\/span><\/p>\n

so the answer is (x+1)(x+2) \u00a0<\/span><\/p>\n

Difference of Squares: <\/b><\/p>\n

If the b value is 0, c is negative, and \u00a0<\/span>the square root of the absolute value of c is a whole number<\/span>, then this is a difference of squares. The numbers are the positive and negative roots of the absolute value of c. Again, skip to the answer and <\/span>insert these numbers straight into the brackets with x.<\/span><\/p>\n

for example, with x^2 – 4<\/span><\/p>\n

since the square root of 4 is 2, <\/span><\/p>\n

the answer is (x-2)(x+2)<\/span><\/p>\n

Pro Tips:<\/b><\/h3>\n

If you are having difficulty with step 4), try using the other version of the rewritten quadratic. \u00a0\u00a0<\/span><\/p>\n

Check your answers by expanding!<\/span><\/p>\n

 <\/p>\n

Interested in English tutoring services<\/a>? Learn more about how we are assisting thousands of students each academic year.<\/p>\n

SchoolTutoring Academy<\/a>\u00a0<\/span>is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in New Haven, CT: visit: Tutoring in Jacksonville, FL.<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Although factoring is a fundamental skill of high school level math, many students experience difficulties. If this includes you, keep reading to become an expert at factoring! \u00a0\u00a0\u00a0\u00a0 The Golden Rule: Common Factor First Common factoring is the process of finding numbers and\/or variables that are a multiple of every term in an expression and […]<\/p>\n","protected":false},"author":17,"featured_media":66961,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-66960","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-uncategorized"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/66960","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/users\/17"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=66960"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/66960\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media\/66961"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=66960"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=66960"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=66960"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}