1) Factorise x2 -6x +8 (the 2 is squared)
2) Hence solve this equation: x2 -6x +8 = 0
Also, what would the line look like on a graph with the equation y = 10/x
Thankyou =)
1) x^2 - 6x + 8 factors are: (x - 2)(x - 4) -->look for possible factors of 8 and determine what will fit to get the middle coefficient of -6. Factors of 8 that fit are -2 * -4. Use FOIL method to check.
2) Now that you have the factors, you can solve the equation x^2 - 6x + 8 = 0
Factored: (x - 2)(x - 4) = 0
Set each factor equal to 0, and solve for each x. You will have 2 possible solutions to this equation.
You can determine what the line would look like for the equation y = 10/x by using a graphing calculator, or by substituting values for x and solving for y. Make sure you get enough points to show the line.
I hope this will help.
If you don't see it, reason as follows. A factorization of an expression like
x^2 -6x +8
is, of course, valid for all values of x. The usual rule of finding two numbers that when multiplied give 8 (and added give -6) amounts to considering the special case x = 0.
But 8 has many factors, so you could try to substitute some other number. If we have a factorization:
x^2 -6x +8 = (x + a)(x + b)
For x = 0 this gives
8 = a*b
But there are many possibilities in this case.
For x = 1 you get:
3 = (1 + a)*(1 + b)
The sum of a and b must be -6. You find the solution by using the factorization 3 = -1*(-3) and you find a = -2 and b = -4
For the function y = x2 - 6x + 8, perform the following tasks:
a)
To factorize x^2 - 6x + 8, look for two numbers that multiply to give 8 and add up to -6 (which is the coefficient of the x term). In this case, the numbers are -2 and -4. Therefore, the factorization is (x - 2)(x - 4).
To solve the equation x^2 - 6x + 8 = 0, set the factored expression equal to zero: (x - 2)(x - 4) = 0. Since the product of two numbers is zero if and only if at least one of the numbers is zero, we can set each factor equal to zero:
x - 2 = 0, which gives x = 2.
x - 4 = 0, which gives x = 4.
Hence, the solutions to the equation x^2 - 6x + 8 = 0 are x = 2 and x = 4.
For the equation y = 10/x, you can determine what the line looks like on a graph by substituting different values of x and solving for y. The graph of this equation is a hyperbola, with the x-axis and y-axis acting as asymptotes. The curve of the hyperbola gets closer to the axes as x approaches positive or negative infinity.
Hope this helps!