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its x^3-3, so if x=3, for instance, the formula is 3*3*3-3=24. if x=5, the formula is 5*5*5-3=122
EDIT:it's already factored if the problem was (^ is the exponent sign)
x^4+x^3+3x+3 (<---example from my homework)
then one would factor as usual (i'm using the british method)
(x^4+x^3)(+3x+3)
x^3(x+1)+3(x+1)
resulting in
(x^3+3)(x+1)
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What is y squared multiplied by y cubed?
y^2 X y^3 = y^(2 + 3) = y^5 You can only do this if the coefficient 'y' is the same for both terms. Remember y^2 = y X y y^3 = y X y X y Hence y^2 X y^3 = y X y X y X y X y = y^5 Similarly for division/subtraction y^3 / y^2 = y^(3 - 2 ) = y^1 = y The power of '1' is trivial and not normally shown. NB You CANNOT do z^2 X y^3 by adding the indices. z^2 X y^3 is (z^2)*(y^3)
Number minus three that equals a multiple of three?
Think of any multiple of three. That number plus three is the next-higher multiple of three. Right? For example, 12 is a multiple of 3 (3 x 4). Add 3 and you get 15 (3 x 5). So 15 - 3 = a multiple of 3. Same thing will work with ANY multiple of 3, no matter how high you go. Can you see why?
What is the prime factorization of 675?
3 x 3 x 3 x 5 x 5
How do you find the probability distribution of x if a fair coin is tosses four times and x is the PRODUCT of the number of heads times the number of tails?
There are 16 possible outcomes, each of which is equally likely. So each has a probability of 1/16 HHHH: X = H*T = 4*0 = 0 HHHT: X = H*T = 3*1 = 3 HHTH: X = H*T = 3*1 = 3 HTHH: X = H*T = 3*1 = 3 THHH: X = H*T = 3*1 = 3 HHTT: X = H*T = 2*2 = 4 HTHT: X = H*T = 2*2 = 4 HTTH: X = H*T = 2*2 = 4 THHT: X = H*T = 2*2 = 4 THTH: X = H*T = 2*2 = 4 TTHH: X = H*T = 2*2 = 4 HTTT: X = H*T = 1*3 = 3 THTT: X = H*T = 1*3 = 3 TTHT: X = H*T = 1*3 = 3 TTTH: X = H*T = 1*3 = 3 TTTT: X = H*T = 0*4 = 0 So, the probability distribution function of X is f(X = 0) = 1/16 f(X = 1) = 4/16 = 1/4 f(X = 2) = 6/16 = 3/8 f(X = 3) = 4/16 = 1/4 f(X = 4 = 1/16 and f(X = x) = 0 for all other x
Examples of cube of a binomial?
(ax + b)^3 = a^3*x^3 + 3*a^2*x^2*b + 3*a*x*b^2 + b^3. Sorry, but it is so clumsy doing this without superscripts!
