Month: November 2017
This week in Math 10 we learned how to factor ugly polynomials (polynomials that aren’t able to be factored with other patterns). There is a simple process to follow and finding the factors of ugly polynomials.
Expression: 12x^2 + 17x + 6
Step 1- Go through the list of patterns and choose which one relates to your expression
Common – any common factors within the expression
Difference of Squares – a squared number subtracted from another squared number
Pattern – does it follow the pattern of polynomial that can be factored (x^2 + x + #)
Easy- no leading coefficients
Ugly- don’t follow any of the patterns
Step 2- Take the leading coefficient and the constant of the expression, multiply them together, and find all the possible ways it can be the product of different numbers.
Step 3- Make a box with 4 squares and put the first term in the top left square and the constant in the bottom right square.
Step 4- Go through the list of the numbers you created and find the one that equals the middle term. If the sign before the constant is a negative then the pairs are different signs. If the the sign before the middle term is a negative, the bigger number of the pair is a negative and if it is a positive then the bigger number is positive. If the sign before the constant is a positive that indicates that both numbers are the same sign.
Step 5- Put the bigger number and its sign in the top right square and the smaller number in the bottom left. With the box completed, go around the box and take out the Greatest Common Factor (The highest number that divides exactly into two or more numbers) with each row and column. The length and width of the box is the factored form of that expression.
This week in Math 10 was all about factoring polynomials into binomials. One thing that stuck with me was factoring different squares ( the difference of squares is a squared number subtracted from another squared number. multiplied by a the same squared number as the start of the last binomial added by the same squared number as the last binomial.
Step 1= find the square root of the terms in the equation 
sqaure root of 100= 10
square root of 25= 5
Step 2= write the equation so that they are conjugates (is formed by changing the sign between two terms in a binomial)
Make it so that the square root of 100x^2 is the first term of both binomials and then the square root of 25 is the second term of the binomials, but one MUST have one addition sign and one subtraction sign
Final answer= (10x – 5)(10x+5)
But sometimes we are faced with sometimes difficult equations that look like aren’t perfect square polynomials, but they are hiddin within
Step 1= In my example I was able to divide 2 by both terms and when I did I was left with
x^2 – 25 which is a difference of perfect sqaures
Then I repeated the steps up top and was left with the
FInal Answer= 2(x-5)(x+5) and just have to remember that the two belongs before the two binomials
This week in Math 10 we started to learn how to factor polynomials which means to break down polynomials into simpler terms so that when they are multiplied together, they equal the original polynomial.
Step 1: In this example that I have created I started off by finding the greatest common factor (the biggest number that divides into
the given numbers) of 14, 21, and 35. I did this buy finding the prime factorization of these three numbers and found the common number which is 7.
Step 2: Then I looked for the greatest common factor of the variables and their exponents by looking at which variables I had which were a and b. Then I looked at the smallest exponent of these variables which were 2 for both a and b
GMF of this equation is 7a^2b^2
Step 3: Then I wanted to be able to use this gmf to equal the original polynomial so I had to find out how many times to multiply this gmf to equal all the terms
