How do you factor #10d^2 + 17d -20#?
We are looking for a solution of the form:
So we need to solve the simultaneous equations:
This has a solution (not unique - this solution is chosen as all terms are integers):
We then have:
Factor: y = 10 x^2 + 17x - 20
Answer: y = (5x - 4)(2x + 5)
I use the new AC Method to factor trinomials (Google, Yahoo Search).
y = 10x^2 + 17x - 20 = 10(x - p)(x - q)
Converted y' = x^2 + 10x - 200.= (x - p')(x - q'). p' and q' have opposite signs.
Factor pairs of (-200) -> (-4, 50)(-8, 25). This sum is 17 = b.
Then p' = -8, and q' = 25.
Then, p = (p')/a = -8/10 = -4/5, and q' = 25/10 = 5/2.
Factored form: y = 10(x - 4/5)(x + 5/2) = (5x - 4)(2x + 5)
Factor by grouping, also called the
Find two numbers that when added equal
Rewrite the equation substituting the sum of
Group the terms into two groups.
Factor out the GCF for each group of terms.
Factor out the common term.