Factoring QuadraticsDate: 06/10/97 at 06:04:33 From: Sebastian Nieto Subject: Factoring Trinomials into Binomials I'm having trouble factoring quadratics, such as 2x^2 - 11x + 15 or 6a^2 + 7a - 5. I probably would've understood this by now, but unfortunately the 'explanations' in my math book are terrible. Date: 06/10/97 at 19:27:31 From: Doctor Anthony Subject: Re: Factoring Trinomials into Binomials The quick method is really trial and error, but with intelligent guesses. We'll start by looking at 2x^2 - 11x + 15. We know the brackets must look like this: (2x )(x ) Then we know the signs must be alike (because of the +15) and the signs must both be negative because of the -11. We can write the brackets as: (2x - )(x - ) The last terms in the brackets must be factors of 15, say 3 and 5, but we must decide where the 3 goes and where the 5 goes. Now look at the middle term -11x. This is obtained by combining the two outer terms in the brackets with the two inner terms. It is immediately obvious that 2 x 3 + 5 x 1 = 11 We complete the factors as: (2x - 5)(x - 3) To check, we combine the two outer terms 2 x 3 = 6 with the two inner terms 5 x 1 = 5 ----- Total 11 Now let's look at 6a^2 + 7a - 5. Step (1) (3a )(2a ) Step (2) (3a 5)(2a 1) or the other way round Step (3) (3a + 5)(2a - 1) or the other way round This happens to be correct because combining two outers 3 x -1 = -3 with two inners 5 x 2 = 10 ----- Total = 7 So the correct factors are: (3a + 5)(2a - 1). With practice you will find that you can write down the factors by inspection. -Doctor Anthony, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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