For letter a, since 3 is in both of the terms, 3 will be included in the gcf.
Fo the literal factors, we choose the one with the least amount of exponent.
We compare the exponent of a^2 and a.
1 < 2. Hence, a will be included in our gcf. Multiplying 3 and a: 3 * a = 3a. So, our gcf = 3a.
We can set it up like this:
3a^2 + 3a = 3a(__ + ___)
For the first blank, divide the first term by the gcf.
3a^2/3a = a
For the second blank, divide the second term by the gcf.
3a/3a = 1
Hence, answer for part A is: 3a(a + 1).
For part b, think of a number which both 14 and 21 is divisible with.
We can prime factorize both of them first.
14 = 7 * 2 and 21 = 7 * 3
Hence, gcf = 7.
For the literal factors we choose the one with the least amount of exponent.
So, for the literal factors gcf = ab.
We then, factor out 7ab.
21ab - 14ab^2 = 7ab(___ + ____)
For the first blank: 21ab/7ab = 3
For the second blank: -14ab^2 = 7ab = -2b.
So, final answer for part B is 7ab(3 - 2b).
the greater commmon divisor beteween (1) and (2) is a, so that: