How do you factor out the greatest common factor?
1. 96x^9y^8+60x^2y^6-84x^4y^4
2. 13m^2-22r^3
3. 24m^8+48m^5-36m^2
1. In the coefficients look for the largest number which evenly divides into all the coefficients of the given terms
2. Variables must have the same base, the greatest common factor is the one with the lowest exponent, eg in #3 it would be m^2
3. Place the coefficients and higest common factor variables out front, follow that with a bracket, and divide all given terms by your greatest common factor then placing the individual answers inside the bracket.
4. The number of terms inside the bracket must match the number of terms your started with.
5. Always test your answer by mentally expanding your final expression to get the original question.
your solution for #3 is
12m^2(2m^6 + 4m^3 - 3)
To factor out the greatest common factor, follow these steps:
1. For the coefficients, find the largest number that evenly divides into all the coefficients of the given terms. In the first expression, 96, 60, and 84 can all be divided by 12. In the second expression, there are no common factors between 13 and 22. In the third expression, 24, 48, and 36 can all be divided by 12.
2. For the variables, look at the exponents of each variable and find the lowest exponent for each variable. For example, in the first expression, the common factors for "x" are x^9, x^2, and x^4. The lowest exponent is x^2. In the second expression, there are no common variables. In the third expression, the common factor for "m" is m^2.
3. After identifying the greatest common factor for both coefficients and variables, place the coefficients and highest common factor variables out front, followed by a bracket. Then divide all given terms by the greatest common factor and place the individual answers inside the bracket. In the first expression, the greatest common factor is 12x^2y^4, so the factored form is 12x^2y^4(8x^7y^4 + 5x^2y^2 - 7x^4). In the second expression, there are no common factors, so it remains unchanged. In the third expression, the greatest common factor is 12m^2, so the factored form is 12m^2(2m^6 + 4m^3 - 3).
4. Make sure that the number of terms inside the bracket matches the number of terms you started with.
5. Always test your answer by mentally expanding your final expression to get the original question and see if they match.
The solution for the third expression is 12m^2(2m^6 + 4m^3 - 3).