Factoring Polynomials using "FOIL": 6x^2 + 17x + 12
- Thread starter Marcie
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Note: The "FOIL" thing is for multiplying, not factoring, binomials, not quadratics or other polynomials. Sorry. 
It sounds as though all you have is the "guess and check" method, which, as you've discovered, is time-consuming and does not inspire confidence. As it happens, neither of the listed quadratics is prime; each can be factored. To learn clear methods for doing this factorising, try here:
. . . . .Google results for "factors quadratic add coefficient"
Note that the "a-b-c" method is what will help you for this harder-case quadratic (where the leading coefficient is not just "1"). But start by learning the method for the easier case, as this will make the method for the harder case a lot easier to understand. :wink:
Have fun!
Eliz.
For a start, I can tell you that, for a polynomial of degree "n", there will be "n" or fewer factors. So there is no possible way for the given quadratic to factor into four binomials. :shock:Marcie said:
It sounds as though all you have is the "guess and check" method, which, as you've discovered, is time-consuming and does not inspire confidence. As it happens, neither of the listed quadratics is prime; each can be factored. To learn clear methods for doing this factorising, try here:
. . . . .Google results for "factors quadratic add coefficient"
Note that the "a-b-c" method is what will help you for this harder-case quadratic (where the leading coefficient is not just "1"). But start by learning the method for the easier case, as this will make the method for the harder case a lot easier to understand. :wink:
Have fun!
Eliz.
Try this:
To factor a quadratic in the form ax^2 + bx + c:
1. Multiply "a" times "c"
2. Find two factors of "ac" that add up to "b"
3. Split the middle term into these two factors. (see example)
4. Complete the factorization.
6x^2 + 17x +12
1. 6 times 12 = 72
2. 72 can be factored into 9 times 8 which adds up to 17 (your middle term)
3. Rewrite the expression by splitting the middle term into your two factors: 6x^2 + 9x + 8x + 12
4. Factor by grouping: 3x(2x + 3) + 4(2x + 3)
Use the distributive property to arrive at: (3x + 4)(2x + 3)
Try this technique on the second quadratic expression you have there.
To factor a quadratic in the form ax^2 + bx + c:
1. Multiply "a" times "c"
2. Find two factors of "ac" that add up to "b"
3. Split the middle term into these two factors. (see example)
4. Complete the factorization.
6x^2 + 17x +12
1. 6 times 12 = 72
2. 72 can be factored into 9 times 8 which adds up to 17 (your middle term)
3. Rewrite the expression by splitting the middle term into your two factors: 6x^2 + 9x + 8x + 12
4. Factor by grouping: 3x(2x + 3) + 4(2x + 3)
Use the distributive property to arrive at: (3x + 4)(2x + 3)
Try this technique on the second quadratic expression you have there.
I've posted an explanation of an easy way to factor polynomials. Factoring Quadratics for Idiots http://lifejelly.org/archives/23
check it out and if you like it, leave a comment!
check it out and if you like it, leave a comment!
speedway_joe
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6x^2+17x+12
=(6x+9)(6x+8)/6
=(3)(2x+3)(2)(3x+4)/6
=(2x+3)(3x+4)
=(6x+9)(6x+8)/6
=(3)(2x+3)(2)(3x+4)/6
=(2x+3)(3x+4)