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The Greatest Common Factor (GCF) is very important when factoring. Later on, you will forget to pull out a GCF and the answer will be wrong. Always look for a GCF before doing anything.
Let's try factoring these:
a.)
The greatest common factor of this expression is 9, because it is the maximum number that both can go into. Let's solve.
This is the simplest this expression can get. This would be your final answer. Let's try the other one.
b.)
The GCF of this one is 12. Let's simplify it.
This is also the simplest you can get it. You can do nothing further. So, your final answers are:
a.)
b.)
First we have to find the slope of the given line. We do that by puttiing the equation into slope-interept form. or solving it for y (same thing). 2x + 4y = -6. We move the 2x over by subtraction to get 4y = -2x - 6. Divide both sides by 4 to get the slope-intercept form we are seeking. . The slope that is perpendicular to that slope of -1/2 is the opposite reciprocal. Therefore, the perpendicular slope is a positive 2/1 or just 2. If this new line goes through the point (2, 5), it goes through the x value of 2 and the y value of 5. We will use those values along with the slope of 2 to solve for b in our slope-intercept equation. That looks like this:
and b = 1. That means our new equation, the one that is perpendicular to the given line, has an equation of y = 2x + 1.