Final answer:
The statements a, c, and e regarding the algebraic expression 3(4u+5)(6+7) are true; b and d are false. The expression contains a coefficient, like terms, and a factor.
Step-by-step explanation:
Let's evaluate the choices given in the question one by one for the expression 3(4u+5)(6+7):
a. In 4u, 4 is a coefficient. This is true because in algebra, a coefficient is a number that multiplies a variable, and here 4 multiplies u.
b. In (4u+5), 4u is a constant. This is false because 4u contains a variable (u), making it a variable term, not a constant. A constant is a fixed number that does not contain any variables.
c. 6 and 7 are like terms. This is true because like terms are terms that contain the same variables raised to the same power. Since 6 and 7 have no variables and are both constants, they can be considered like terms.
d. (4u+5) is written as a sum of three terms. This is false because it is a sum of only two terms: 4u and 5.
e. 4u is a factor. This is true because a factor is a number or expression that multiplies with others to give a product, and 4u is being multiplied by 3 and (6+7).
f. None of these are true. This is false because as noted above, options a, c, and e are true.
By eliminating terms that do not conform to the definitions, we simplify the algebra and can determine the accurate statements about the algebraic expression given.