// Numbas version: exam_results_page_options {"name": "HELM Book 1.3.4 exercises", "metadata": {"description": "

HELM Book 1.3.4 exercises

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Factorise a 2-term expression by pulling out a numeric gcd. Part of HELM Book 1.3

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

Practise these questions repeatedly until you can quickly, confidently and correctly factorise the expressions.

The questions will change each time you click the \"Try another question like this one\" button.

To enter $3ab(7+4b^2)$, type 3a*b*(7+4b^2)

", "advice": "

$\\var{q1c[2]*q1c[0]}$ and $\\var{q1c[2]*q1c[1]}$ have a common factor of $\\var{q1gcd}$, so

$\\var{q1expr}=\\var{q1ans}$

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Factorise $\\var{q1expr}$. Check your answer by removing the brackets again.

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Factorise a 2-term expression where the gcd can be alphanumeric. Part of HELM Book 1.3

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Practise these questions repeatedly until you can quickly, confidently and correctly factorise the expressions.

", "advice": "

$\\var{simplify(expression(q2terms[q2termidx]),\"all\")}$ and $\\var{simplify(expression(q2terms[mod(q2termidx+1,2)]),\"all\")}$ have a common factor of $\\var{fullgcd}$

so $\\var{q2expr}=\\var{q2ans}$

In these expressions, the common factor consists of one number and one variable.

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The two terms are randomly ordered, but can look like one of four cases:

* m.a + n.a.b

* m.a.b + n.a.c or m.a^2 + n.a.c

* m.a.b + n.a.c.d or m.a.b + n.a^2.c

* m.a.b + n.a.b.c or m.a.b + n.a^2.c

* m.a + n.b.c

Here m and n are numbers, and a,b,c are variables

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This chooses the order in which the terms are written.

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Terms with the common factors removed.

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A helping variable used to extract the alphanumeric gcd from q2ans.

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Factorise $\\var{q2expr}$. Check your answer by removing the brackets again.

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Explain why one variable is a factor but the other is not. Factorise the expression, whose factor is alphanumeric. Part of HELM Book 1.3

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

Practise these questions repeatedly until you can quickly, confidently and correctly factorise the expressions.

", "advice": "

$\\var{v1e}$ is a factor of every term of $\\var{q3expr}$ but $\\var{v2e}$ does not appear in every term.

Hence $\\var{v1e}$ is a factor of $\\var{q3expr}$ but $\\var{v2e}$ is not.

The greatest divisor appearing in every term is $\\var{fullgcd}$.

So $\\var{q3expr}=\\var{q3ans}$

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0 is a linear factor

1 is a square factor

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used to get the full alphanumeric gcd out of q3ans

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used in the advice

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used for display in the advice

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used for display in the advice

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Explain why $\\var{v1e}$ is a factor of $\\var{q3expr}$ but $\\var{v2e}$ is not.

Factorise $\\var{q3expr}$.

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Work through these practice questions. You are encouraged to try each question multiple times as the expressions in each question will change each time you try it.

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