Year 9 Maths Algebraic Techniques

Factorising Non Monic Quadratic Trinomials

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Questions

Question 1

42873

Factorise $ 3{x}^{2}+13{x}+4 $

Answer

$(3x+1)(x+4)$

Worked Solution

\[3x^2+13x+4\]\[4\times 3 =12\]
We have to find the numbers whose sum is $13$ and the product is $12$. The numbers are $12$ and $1$.
$$
\begin{aligned}
&=3x^2+12x+x+4\\
&=3x(x+4)+1(x+4)\\
&=(3x+1)(x+4)
\end{aligned}
$$

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