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<!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 data-main="../local-only/main.js" src="../local-only/require.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() &lt; 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>
</div>
<p class="question">
Factor the expression below completely. All coefficients should be integers.
</p>
<p class="problem">
<code><var>expr(["+", ["*", A, "x"], B])</var></code>
</p>
<div class="solution" data-type="expression" data-same-form="">
<var>SOLUTION</var>
</div>
<div class="hints">
<p>
To factor a binomial, you should first 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>.<br>
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 class="final_answer" data-if="IS_IRREDUCIBLE">
Therefore the answer is the original expression,
<code><var>SOLUTION</var></code>.
</p>
<p data-if="!IS_IRREDUCIBLE">
So we can factor out the <code><var>GCD</var></code>.
</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 class="final_answer" data-if="!IS_IRREDUCIBLE">
So the factored expression is
<code><var>SOLUTION</var></code>.
</p>
</div>
</div>
</div>
</div>
</body>
</html>