How do I factor a polynomial?
I am completely confused about how to factor two kinds of polynomials. The first are ones such as 6x^2-5x+1.
I can't group because there aren't four and I know there is a faster way than guessing and checking but I don't remember. Can someone help me out?
The other kind I am having trouble with are the kind that are like 15x^2-4xy-4y^2.
Any help is appreciated. Thanks.
Update:How do I get said answers?
Comments
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(1.)
6x² - 5x + 1 ← the general form is ax² + bx + c
To do these you need, first, to find two factors of a·c that will add to b.
So, you need two factors of 6 that will add to -5.
Those factors would be -3 and -2.
( 1)( 1) ← Think FOIL ... Last is 1 ... it must be 1·1
(3x 1)(2x 1) ← you need 3 and 2 to get a 5 for b ... think a = 6 = 3·2
(3x - 1)(2x - 1) ← put in the signs necessary to get 6, -5, and +1 for a,b, and c
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(2.)
15x² - 4xy - 4y²
The x² and y² tell you the binomials will be in x and y.
Also, as in (1), you need two factors of -60, that's (15)(-4), that will add to -4.
Those factors are -10 and 6.
Notice that -10 and 15 are divisible by 5, where 6 and 4 are not.
So, break 15 up into 3 and 5.
(3x ) (5x )
(3x - 2 ) (5x ) ← think FOIL...to get the -10, pair up -2 with the 5
(3x - 2 ) (5x + 2 ) ← think FOIL...to get the -4 as Last, use +2
(3x - 2y)(5x + 2y) ← don't forget the y's & check by FOILing
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(3x-1)(2x-1)
(5x-2y)(3x-2y)