John R. answered • 10/13/12
John R: Math, Science, and History Teacher
To begin factor this problem, break down your coefficeients into prime factors so that you can see what common factors there are (e.g. The prime factors of 12 are 2 X 2 X 3 and the prime factors of 27 are 3 X 3 X 3).
2 X 2 X 3 z8 - 3 X 3 X 3
or 3 X 4z8 -3 X 9
factoring out a 3 we get 3(4z8 - 9)
If you look at each term in the parenthesis, you may notice that they are both perfect squares. The first term is (2z4)2 and the second term is 32. In any binomial (algebraic expression that has two terms) that a perfect square is subtracted from another perfect square, the factors will be the square root of the first term minus the square root of the second and the square root of the first term plus the square root of the second.
In other words 3[(2z4)2 - 32] = 3(2z4 - 3)(2z4 + 3)
The final answer is 3(2z4 - 3)(2z4 + 3)
John R.
Since the sign on 12 is +, you need to find the terms that add of to 7. The factors are (b - 3) and (b - 4)
10/13/12
Kristine D.
Thanks John, I thought there had to be a difference of 7, not add up to 7.
10/13/12
John R.
The sign on the third term (in this case 12) determines whether the second term (in this case 7) is a sum or a difference.
10/13/12
Kristine D.
Thanks John. Butthis one has got me thrown for a loop. b^2 - 7b + 12. Now I know the factors of 12 are (1 and 12) (2 and 6) and (3 and 4) but none of them have a difference of 7.
10/13/12