1.Find the greatest common factor in this problem.
12a3b2, 18a2b3, 6a4b4
2.Factor each of the following polynomials.
4s _ 6st _ 14st2
Question 2 has a typo. Rewrite question 2 because it does not make sense.
Question 1:
Find the greatest common factor in this problem.
12a^3b^2, 18a^2b^3, 6a^4b^4
GCF = 36a^4b^4
Done!
To find the greatest common factor (GCF) of a set of terms, follow these steps:
1. Write down the prime factors of all the terms.
For the given problem, the terms are: 12a^3b^2, 18a^2b^3, and 6a^4b^4.
The prime factorization of these terms is as follows:
12a^3b^2 = 2² * 3 * a^3 * b^2
18a^2b^3 = 2 * 3² * a^2 * b^3
6a^4b^4 = 2 * 3 * a^4 * b^4
2. Identify the common factors.
Look for factors that are present in all the terms.
In this case, we can see that the common factors are 2 and 3.
3. Determine the lowest exponent for each variable.
Compare the exponents of each variable (a and b) in the terms.
For a, the lowest exponent is 2 (from the term 18a^2b^3).
For b, the lowest exponent is 2 (from the terms 12a^3b^2 and 6a^4b^4).
4. Combine the common factors with the lowest exponents.
The GCF is the product of the common factors with the lowest exponents.
Therefore, the GCF of 12a^3b^2, 18a^2b^3, and 6a^4b^4 is 2 * 3 * a^2 * b^2.
Now, let's move on to factoring the given polynomial: 4s - 6st - 14st^2.
To factor the polynomial, follow these steps:
1. Identify the greatest common factor (GCF) of all the terms.
In this case, the GCF is 2s because it is the largest common term in all the terms.
2. Divide each term by the GCF.
Divide 4s by 2s, which gives 2.
Divide -6st by 2s, which gives -3t.
Divide -14st^2 by 2s, which gives -7t^2.
3. Write the factored polynomial using the GCF as a factor.
The factored polynomial is: 2s(1 - 3t - 7t^2).
Therefore, the factored form of the polynomial 4s - 6st - 14st^2 is 2s(1 - 3t - 7t^2).