Dear Uncle Colin,
How would you factorise $63x^2 + 32x – 63$? I tried the method where you multiply $a$ and $c$ (it gives you -3969) – but I’m not sure how to find factors of that that sum to 32!
Factors Are Troublesomely Oversized, Urgh
Hi, FATOU, and thanks for your message!
When the numbers in a quadratic like this get large (in mental arithmetic terms, at least), I try not to think about the number itself, but about its prime factorisation.
In this case, we know -3969 is $-63 \times 63$, making it $-3^2 \times 7 \times 3^2 \times 7$ or $-3^4 \times 7^2$.
How does that help?…
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