QUESTION 1: Introduction to the GCF of two monomials
Find the greatest common factor of: 12x^2 and 8x^4
EXPLANATION:
The GCF of 12 and 8 is 4
The GCF of x^2 and x^4 is x^2
So, the GCF of 12x^2 and 8x^4 is 4x^2
ANSWER: 4x^2
QUESTION 2: Factoring a difference of squares in one variable
Factor: u^2 – 4
EXPLANATION:
Here is the factoring formula for the difference of squares
A^2 – B^2 = (A + B)(A - B)
We can use this for the current
problem
u^2 – 4 = u^2 – 2^2 Writing as A^2 – B^2, with A=u and B=2
= (u + 2)(u - 2) Using the difference of squares formula
ANSWER: (u +
2)(u - 2)
QUESTION 3: Factoring a quadratic with leading coefficient greater than 1(Problem type 1)
Factor: 3y^2 – 4y -7
EXPLANATION:
In this question we will factor using a method often called Trial and Error
The coefficient of y^2 is 3
Using whole numbers, only 1 and 3
have a product of 3
So we'll look for integers n
and m that satisfy the following
3y^2 – 4y -7 = (1y + m)(3y
+ n)
Using FOIL to expand the
right-hand side of this equation, we get the following
m*n =
-7 and n + 3m = -4
We'll find all integers m
and n such that n*m = -7
Then we'll check to see if n
+ 3m = -4
n m
n+3m
1 -7 -4
-1 7 4
-7 1 -20
7 -1 20
From the table, we find that m = 1 and n = -7
work
So we have the following:
3y^2 – 4y -7 = (y + m)(3y + n)
= (y + 1)(3y – 7)
ANSWER: (y +
1)(3y – 7)
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