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3w^2 - 8w + 4 = (3w -2) (w-2) So 3w-2=0, then 3w=2, so w=2/3, w-2=0, so w=2. Your solutions are w=2/3 and w=2.
The roots (or solutions) are the numbers that 'w' must be in order to make the equation true.Since the highest power of 'w' in the equation is the first power, there's only one solution.3w - 14 - 6 = 21Combine the -14 and the -6 on the left side:3w - 20 = 21Add 20 to each side:3w = 41Divide each side by 3 :w = 41/3 = 132/3
3w
It seems as if the greatest common factor of those two terms would be 3w2,but that's only true if 'w' is greater than '1'. If 'w' is less than '1', then their GCFis 3 .
5x**2-30x-801. Remove common term (and ignore til end):5(x**2-6x-16)2. Multiply first and third terms1*-16=-163. Factor product of first and third terms-16, 1-8, 2-4, 416, -18, -24. Choose factors whose sum is equal to second term-8+2=-65. Rewrite equation using factorsx**2-8x+2x-166. Halve the expressionx**2-8x2x-167. Factor each halfx**2-8x --> x(x-8)2x-16 --> 2(x-8)8. Recombinex(x-8)+2(x-8)9. Factor out common term:(x-8)(x+2)10. Reintroduce part from beginning5(x-8)(x+2)