Blog Post Week 10

For math this week we learned about using polynomials to factor trinomials and using them to find the difference of squares.

If we wanted to determine the factor to the expression x^2-10x+24 we would want to find two numbers that would both multiply together to create 24 and add together to create -10, since -4 and -6 multiply to create 24 and add to make -10 our factor is (x-6)(x-4) because x and x multiply together and with -6 and -4 to create x^2 and -10x.

We can use this same method to factor and determine the difference of squares. When we use this method to find the sides of a floor we want to end up with 2 binomials so two of the numbers must equal 0 if added together, so for the expression 9x^2-25 the expression for the length and width of the square equals (3x-5)(3x+5). If we were to find the factor of 20x^{2}y-45y even though they both are unable to equally factor by themselves if we divide the equation by 5y we get numbers that can, creating the expression 5y(4x^2-9) which is factored as 5y(2x-3)(2x+3).

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