How do you factor #2d^2-7d-15#?
This may be factorized as a trinomial to obtain the factors
To obtain this you look at the coefficient of the first term, 2, and see what its factors are. There is only 1 option,
Then look at the coefficient of the last term, 15, and there are a 2 options here namely :
You now need to combine the options such that the sum of the factors when cross-multiplied give you the middle term of
The only option is
and so therefore the factors are the rows of the matrix shown.
To factor a quadratic function with a leading coefficient greater than 1, do the following steps:
- Multiply the leading coefficient and the constant:
- What two numbers would multiply to give you -
#30#and add to give you - #7#?
- Since we multiplied the constant by 2, divide the numbers you got above by 2:
So, instead of
- Final factors: