Which is the factorization of 8x2 13x – 6? (8x – 3)(x 2) (x – 6)(8x 1) (2x – 2)(4x 3) (4x – 1)(2x 6)
2 answers:
So than there are
8x^2 +13x -6 = (8x-3)(x+2)
hope this will help you
we have
![8x^2+13x - 6](https://tex.z-dn.net/?f=%208x%5E2%2B13x%20-%206%20)
Equate the function to zero
![8x^2+13x - 6=0](https://tex.z-dn.net/?f=%208x%5E2%2B13x%20-%206%3D0%20)
Group terms that contain the same variable, and move the constant to the opposite side of the equation
![8x^2+13x = 6](https://tex.z-dn.net/?f=%208x%5E2%2B13x%20%3D%206%20)
Factor the leading coefficient
![8(x^2+\frac{13}{8}x) = 6](https://tex.z-dn.net/?f=%208%28x%5E2%2B%5Cfrac%7B13%7D%7B8%7Dx%29%20%3D%206%20%20)
Complete the square. Remember to balance the equation by adding the same constants to each side.
![8(x^2+\frac{13}{8}x) = 6](https://tex.z-dn.net/?f=%208%28x%5E2%2B%5Cfrac%7B13%7D%7B8%7Dx%29%20%3D%206%20%20)
![8(x^2+\frac{13}{8}x+\frac{169}{256}) = 6 +\frac{169}{32} \\ \\ 8(x+\frac{13}{16} )^{2} =\frac{361}{32} \\ \\ (x+\frac{13}{16} )^{2} =\frac{361}{256}\\ \\ (x+\frac{13}{16} ) =(+/-)\sqrt{\frac{361}{256}} \\ \\ (x+\frac{13}{16} ) =(+/-)\frac{19}{16} \\ \\ x1=-\frac{13}{16} +\frac{19}{16} =\frac{6}{16}\\ \\ x2=-\frac{13}{16} -\frac{19}{16}=-2](https://tex.z-dn.net/?f=%208%28x%5E2%2B%5Cfrac%7B13%7D%7B8%7Dx%2B%5Cfrac%7B169%7D%7B256%7D%29%20%3D%206%20%2B%5Cfrac%7B169%7D%7B32%7D%20%5C%5C%20%5C%5C%208%28x%2B%5Cfrac%7B13%7D%7B16%7D%20%29%5E%7B2%7D%20%3D%5Cfrac%7B361%7D%7B32%7D%20%5C%5C%20%5C%5C%20%28x%2B%5Cfrac%7B13%7D%7B16%7D%20%29%5E%7B2%7D%20%3D%5Cfrac%7B361%7D%7B256%7D%5C%5C%20%5C%5C%20%28x%2B%5Cfrac%7B13%7D%7B16%7D%20%29%20%3D%28%2B%2F-%29%5Csqrt%7B%5Cfrac%7B361%7D%7B256%7D%7D%20%5C%5C%20%5C%5C%20%28x%2B%5Cfrac%7B13%7D%7B16%7D%20%29%20%3D%28%2B%2F-%29%5Cfrac%7B19%7D%7B16%7D%20%20%5C%5C%20%5C%5C%20x1%3D-%5Cfrac%7B13%7D%7B16%7D%20%2B%5Cfrac%7B19%7D%7B16%7D%20%3D%5Cfrac%7B6%7D%7B16%7D%5C%5C%20%5C%5C%20x2%3D-%5Cfrac%7B13%7D%7B16%7D%20-%5Cfrac%7B19%7D%7B16%7D%3D-2%20%20)
the factorization is equal to
![8*(x-\frac{6}{16} )*(x+2)=(8x-3)*(x+2)](https://tex.z-dn.net/?f=%208%2A%28x-%5Cfrac%7B6%7D%7B16%7D%20%29%2A%28x%2B2%29%3D%288x-3%29%2A%28x%2B2%29%20)
therefore
<u>the answer is</u>
![(8x-3)*(x+2)](https://tex.z-dn.net/?f=%20%288x-3%29%2A%28x%2B2%29%20)
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