Calculating the Greatest Common Factor

The first step in solving this algebra is to open the brackets. We multiply the negative sign outside the bracket with the sign inside the bracket. Since negative sign multiplied by negative sign lead to positive and negative multiple by positive sign result in positive, the solution after opening the brackets is shown below.

3m3-6+2m3-m2-3

We then collect the like terms and either sum or subtract as dictated by the preceding sign

3m3+2m3-m2-6-3

5m3-m2-9

Based on this result, Katie was right in her calculation.

2.  Divide (x2 – 3x – 33)/ (x – 4).

In this case, we can use long polynomial division

The divided is (x2 – 3x – 33), and the divisor is (x – 4).

We first multiply the divisor by x1

to get x2-4x

We then proceed to subtract x2-4x from x2 – 3x – 33.

The result would x-33

The next step is to multiply divisor (x – 4) by x0 to get x – 4

We then proceed to subtract the output (x-4) from x-33 to get -29’

The quotient = x+1 while the reminder = -29

Thus, the trinomial cannot be factored and the solution = (x2 – 3x – 33)/ (x – 4)

3.  (3x + 7)2 = 9x2 + 49 (incorrect)

We employ the common expression (a+b)2 = (a+b) (a+b) = a2+ab+ab+b2 = a2+2ab+b2

In this case, a=3x and b=7

Therefore, correct solution = (3x)2+2*3x*7+72 = 9x2 +42x+49

4.  Factor 100x2 – 121

a2-b2 = (a – b) (a + b)

In this case, a2 = 100x2 and b2=121

We get the square root of each of the element of the binomial

√ 100x2 = 10x and √121 = 11

Therefore, (100x2 – 121) = (10x-11) (10x-11)

5.  Factor 24x3 - 81 

First determine the greatest common factor of 24x3 – 81.

In this case, the GCF = 3

24x3 - 81 = 3(8x3-27)

3(8x3-27) = 3((2x)3

– (3)3)

But since: a3 –b3 = (a-b) (a2-ab+b2)

(3(2x)3 – 33) = 3(2x -3) (4x2-6x +9)