Which statements about the factors of the terms in the expression 20a+15ab+24b are true? the factors common to 20a and 15ab are 1, 5, a, and b. the factors common to 20a and 15ab are 1, 5, and a. the factors common to 15ab and 24b are 1, 3, a, and b. the factors common to 15ab and 24b are 1, 3, and b. the factors common to 20a and 24b are 1, 2, 4, a, and b. the factors common to 20a and 24b are 1, 2, and 4. the gcf of the expression is ab. the gcf of the expression is 1

1) Expression given: 20a+15ab+24b


2) Greates common factor GFC:

i) Coefficients:

20 = 2² × 5 × 1

15 = 3 × 5 × 1

24 = 2³ × 8 × 1

GCF = common numbers raised to the lower power = 1.


ii) Letters:
a
ab
b
Since, none letter is in the three terms, then there is not common letter as GFC.

iii) Conclusion the GCF is 1.

3) Let's see every option of the list:


i) The factors common to 20a and 15ab are 1, 5, a, and b.


FALSE: becasue b is not in 20a.

ii) The factors common to 20a and 15ab are 1, 5, and a.


TRUE: 1, 5, and a are in contained in both terms.

iii) The factors common to 15ab and 24b are 1, 3, a, and b.


FALSE: a is not in 24b

iv) The factors common to 15ab and 24b are 1, 3, and b.


TRUE: 1, 3, and b are contained in both terms.

v) The factors common to 20a and 24b are 1, 2, 4, a, and b.


FALSE: a is not in 24b and b is not in 20a.

vi) The factors common to 20a and 24b are 1, 2, and 4.


TRUE: 1, 2, and 4 are contained in both terms.

vii) The GCF of the expression is ab.


FALSE: as seen above ab is not a common factor.

viii) The GCF of the expression is 1


TRUE: it was proved above.