Factor completely and explain please…?
6r^2+17rp+12p^2
&
12t^2-30tv-42v^2
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Treat the first as 6x^2 + 17x + 12. Factorise that, and then put the r and p factors into position as I explained in your previous question.
Similarly, reduce the second to 12x^2 – 30x – 42. Notice first that you can extract a factor of 6. That makes things simpler. When you’ve done that, put the t and v in place.
As explained previously:
If ax^2 + bx + c can be factorised into (px + q)(rx + s), an expression of the form ax^2 + bxy + cy^2 can be factorised into (px + qy)(rx + sy). The technique is exactly the same. You just have the additional variable making the problem look a little more difficult
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Find the factor for the first and last term. Then find a combination between the two sets that will add or subtract to get your middle number.
6r^2+17rp+12p^2
(2r + 3p)(3r + 4p)
12t^2-30tv-42v^2
6(2t^2 – 5tv – 7v^2)
6(2t – 7v)(t + v)
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