Clare's copy of Factorising a monic quadratic

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Question 1

Factorise the following into linear factors. That is, write the quadratic as a product of terms that look like $ax+b$ where $a$ and $b$ are real numbers.

$\simplify{x^2+{linear}x+{const}}$ = interpreted as $\displaystyle{}$ Expected answer:interpreted as $\displaystyle{\left ( x + 6 \right ) \left ( x + 4 \right )}$ .

Since $(x+a)(x+b)=x^2+(a+b)x+ab$ , when we are factorising a quadratic, such as $x^2+cx+d$ , we must find the numbers $a$ and $b$ such that $c=a+b$ and $d=ab$ .

In the case of $\simplify{x^2+{linear}x+{const}}$ we ask

what two numbers add to give $\var{linear}$ and multiply to give $\var{const}$ ?

Therefore the numbers must be $\var{a}$ and $\var{b}$ , that is

$\simplify{x^2+{linear}x+{const}}=(\simplify{x+{a}})(\simplify{x+{b}}).$

You can check this by expanding the binomial product.

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Clare's copy of Factorising a monic quadratic

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