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Use regex answer type to avoid dependency on math-model
Summary: I changed this to use regexs to check the answer and made it pretty liberal (i.e. it's always ok to run a -1 through everything) Differential Revision: http://phabricator.khanacademy.org/D566
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,105 @@ | ||
| <!DOCTYPE html> | ||
| <html data-require="math math-format word-problems expressions"> | ||
| <head> | ||
| <meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> | ||
| <title>Factoring linear binomials</title> | ||
| <script src="../khan-exercise.js"></script> | ||
| </head> | ||
| <body> | ||
| <div class="exercise"> | ||
| <div class="problems"> | ||
| <div> | ||
| <div class="vars"> | ||
| <var id="A">randRange(2, 9)</var> | ||
| <var id="IS_IRREDUCIBLE">random() < 0.2</var> | ||
|
|
||
| <div data-ensure="(GCD === 1) === IS_IRREDUCIBLE"> | ||
| <var id="B">randRangeExclude(-20, 20, [-1, 0, 1])</var> | ||
| <var id="GCD">getGCD(A, B)</var> | ||
| </div> | ||
| <var id="SOLUTION"> | ||
| IS_IRREDUCIBLE ? plus(A + "x", B) : | ||
| GCD + "(" + plus(A / GCD + "x", B / GCD) + ")" | ||
| </var> | ||
| <var id="Ax_FACTORS"> | ||
| toSentenceTex(getFactors(abs(A)).concat(["x"])) | ||
| </var> | ||
| <var id="B_FACTORS"> | ||
| toSentenceTex(getFactors(abs(B))) | ||
| </var> | ||
| <var id="TERM1">GCD</var> | ||
| <var id="TERM1N">"[-\\u2212]" + GCD</var> | ||
| <var id="TERM2">"(?:" + (A < 0 ? "[-\\u2212]" : "") + abs(A / GCD) + (A / GCD === 1 ? "|" : "" ) + (A / GCD === -1 ? "|[-\\u2212]" : "") + ")\\s*x"</var> | ||
| <var id="TERM2N">"(?:" + (A > 0 ? "[-\\u2212]" : "") + abs(A / GCD) + (A / GCD === -1 ? "|" : "" ) + (A / GCD === 1 ? "|[-\\u2212]" : "") + ")\\s*x"</var> | ||
| <var id="TERM3">(B < 0 ? "[-\\u2212]" : "\\+") + "\\s*" + abs(B / GCD)</var> | ||
| <var id="TERM3N">(B > 0 ? "[-\\u2212]" : "\\+") + "\\s*" + abs(B / GCD)</var> | ||
| </div> | ||
| <p class="question"> | ||
| Write the following expression in its most factored form: | ||
| </p> | ||
| <p class="problem"> | ||
| <code><var>expr(["+", ["*", A, "x"], B])</var></code> | ||
| </p> | ||
| <div class="solution" data-type="set"> | ||
| <div data-if="IS_IRREDUCIBLE" data-unwrap> | ||
| <div class="set-sol" data-type="regex">^\s*<var>TERM2</var>\s*<var>TERM3</var>\s*$</div> | ||
| <div class="set-sol" data-type="regex">^\s*<var>TERM2N</var>\s*<var>TERM3N</var>\s*$</div> | ||
| <div class="set-sol" data-type="regex">^\s*\(\s*<var>TERM2</var>\s*<var>TERM3</var>\s*\)\s*$</div> | ||
| <div class="set-sol" data-type="regex">^\s*\(\s*<var>TERM2N</var>\s*<var>TERM3N</var>\s*\)\s*$</div> | ||
| </div> | ||
| <div data-else data-unwrap> | ||
| <div class="set-sol" data-type="regex">^\s*<var>TERM1</var>\s*\(\s*<var>TERM2</var>\s*<var>TERM3</var>\s*\)\s*$</div> | ||
| <div class="set-sol" data-type="regex">^\s*<var>TERM1N</var>\s*\(\s*<var>TERM2N</var>\s*<var>TERM3N</var>\s*\)\s*$</div> | ||
| </div> | ||
| <div class="input-format"><span class="entry"></span></div> | ||
| <div class="example"> | ||
| a factored expression, like <b>5(x+2)</b> | ||
| </div> | ||
| </div> | ||
| <div class="hints"> | ||
| <p> | ||
| To factor a polynomial, you should first try to find | ||
| the greatest common factor of all the terms. | ||
| </p> | ||
| <p> | ||
| The factors of <code><var>A</var>x</code> are | ||
| <var>Ax_FACTORS</var> and the factors of | ||
| <code><var>B</var></code> are <var>B_FACTORS</var>. | ||
| </p> | ||
| <p> | ||
| The greatest common factor of <code><var>A</var>x</code> | ||
| and <code><var>B</var></code> is | ||
| <code><var>GCD</var></code>. | ||
| </p> | ||
|
|
||
| <p data-if="IS_IRREDUCIBLE"> | ||
| Since the greatest common factor is <code>1</code>, | ||
| the expression is already in its most factored form. | ||
| </p> | ||
| <p data-if="IS_IRREDUCIBLE" class="final_answer"> | ||
| Therefore the answer is the original expression, | ||
| <code><var>SOLUTION</var></code>. | ||
| </p> | ||
|
|
||
| <p data-if="!IS_IRREDUCIBLE"> | ||
| We can factor out the <code><var>GCD</var></code> and | ||
| put it before the parenthesis. | ||
| </p> | ||
| <p data-if="!IS_IRREDUCIBLE"> | ||
| If we divide each of the terms in the original | ||
| expression by <code><var>GCD</var></code> we get | ||
| <code>\dfrac{<var>A</var>x}{<var>GCD</var>} = | ||
| <var>plus((A/GCD) + "x")</var></code> and | ||
| <code>\dfrac{<var>B</var>}{<var>GCD</var>} = | ||
| <var>B/GCD</var></code>. | ||
| </p> | ||
| <p data-if="!IS_IRREDUCIBLE" class="final_answer"> | ||
| So the factored expression is | ||
| <code><var>SOLUTION</var></code>. | ||
| </p> | ||
| </div> | ||
| </div> | ||
| </div> | ||
| </div> | ||
| </body> | ||
| </html> |